permutation-groups.py

import datasets
import json
import os
import pyarrow as pa

_DESCRIPTION = "A comprehensive collection of permutation composition datasets for various mathematical groups including symmetric, alternating, cyclic, dihedral, and sporadic groups."
_HOMEPAGE = "https://huggingface.co/datasets/BeeGass/permutation-groups"
_LICENSE = "MIT"

class PermutationGroupsConfig(datasets.BuilderConfig):
    def __init__(self, *args, group_name=None, group_degree=None, group_order=None, data_dir=None, max_len=None, **kwargs):
        super().__init__(*args, **kwargs)
        self.group_name = group_name
        self.group_degree = group_degree
        self.group_order = group_order
        self.data_dir = data_dir
        self.max_len = max_len

class PermutationGroups(datasets.ArrowBasedBuilder):
    """Use ArrowBasedBuilder for better performance with Arrow files."""
    
    VERSION = datasets.Version("2.0.0")

    BUILDER_CONFIGS = [
        PermutationGroupsConfig(
            name="s3_data",
            description="Symmetric Group S3 (order 6).",
            group_name="S3",
            group_degree=3,
            group_order=6,
            data_dir="data/s3_data",
        ),
        PermutationGroupsConfig(
            name="s4_data",
            description="Symmetric Group S4 (order 24).",
            group_name="S4",
            group_degree=4,
            group_order=24,
            data_dir="data/s4_data",
        ),
        PermutationGroupsConfig(
            name="s5_data",
            description="Symmetric Group S5 (order 120).",
            group_name="S5",
            group_degree=5,
            group_order=120,
            data_dir="data/s5_data",
        ),
        PermutationGroupsConfig(
            name="s6_data",
            description="Symmetric Group S6 (order 720).",
            group_name="S6",
            group_degree=6,
            group_order=720,
            data_dir="data/s6_data",
        ),
        PermutationGroupsConfig(
            name="s7_data",
            description="Symmetric Group S7 (order 5040).",
            group_name="S7",
            group_degree=7,
            group_order=5040,
            data_dir="data/s7_data",
        ),
        PermutationGroupsConfig(
            name="a3_data",
            description="Alternating Group A3 (order 3).",
            group_name="A3",
            group_degree=3,
            group_order=3,
            data_dir="data/a3_data",
        ),
        PermutationGroupsConfig(
            name="a4_data",
            description="Alternating Group A4 (order 12).",
            group_name="A4",
            group_degree=4,
            group_order=12,
            data_dir="data/a4_data",
        ),
        PermutationGroupsConfig(
            name="a5_data",
            description="Alternating Group A5 (order 60).",
            group_name="A5",
            group_degree=5,
            group_order=60,
            data_dir="data/a5_data",
        ),
        PermutationGroupsConfig(
            name="a6_data",
            description="Alternating Group A6 (order 360).",
            group_name="A6",
            group_degree=6,
            group_order=360,
            data_dir="data/a6_data",
        ),
        PermutationGroupsConfig(
            name="a7_data",
            description="Alternating Group A7 (order 2520).",
            group_name="A7",
            group_degree=7,
            group_order=2520,
            data_dir="data/a7_data",
        ),
        PermutationGroupsConfig(
            name="c3_data",
            description="Cyclic Group C3 (order 3).",
            group_name="C3",
            group_degree=3,
            group_order=3,
            data_dir="data/c3_data",
        ),
        PermutationGroupsConfig(
            name="c4_data",
            description="Cyclic Group C4 (order 4).",
            group_name="C4",
            group_degree=4,
            group_order=4,
            data_dir="data/c4_data",
        ),
        PermutationGroupsConfig(
            name="c5_data",
            description="Cyclic Group C5 (order 5).",
            group_name="C5",
            group_degree=5,
            group_order=5,
            data_dir="data/c5_data",
        ),
        PermutationGroupsConfig(
            name="c6_data",
            description="Cyclic Group C6 (order 6).",
            group_name="C6",
            group_degree=6,
            group_order=6,
            data_dir="data/c6_data",
        ),
        PermutationGroupsConfig(
            name="c7_data",
            description="Cyclic Group C7 (order 7).",
            group_name="C7",
            group_degree=7,
            group_order=7,
            data_dir="data/c7_data",
        ),
        PermutationGroupsConfig(
            name="c8_data",
            description="Cyclic Group C8 (order 8).",
            group_name="C8",
            group_degree=8,
            group_order=8,
            data_dir="data/c8_data",
        ),
        PermutationGroupsConfig(
            name="c10_data",
            description="Cyclic Group C10 (order 10).",
            group_name="C10",
            group_degree=10,
            group_order=10,
            data_dir="data/c10_data",
        ),
        PermutationGroupsConfig(
            name="c12_data",
            description="Cyclic Group C12 (order 12).",
            group_name="C12",
            group_degree=12,
            group_order=12,
            data_dir="data/c12_data",
        ),
        PermutationGroupsConfig(
            name="z3_data",
            description="Cyclic Group Z3 (order 3).",
            group_name="Z3",
            group_degree=3,
            group_order=3,
            data_dir="data/z3_data",
        ),
        PermutationGroupsConfig(
            name="z4_data",
            description="Cyclic Group Z4 (order 4).",
            group_name="Z4",
            group_degree=4,
            group_order=4,
            data_dir="data/z4_data",
        ),
        PermutationGroupsConfig(
            name="z5_data",
            description="Cyclic Group Z5 (order 5).",
            group_name="Z5",
            group_degree=5,
            group_order=5,
            data_dir="data/z5_data",
        ),
        PermutationGroupsConfig(
            name="z6_data",
            description="Cyclic Group Z6 (order 6).",
            group_name="Z6",
            group_degree=6,
            group_order=6,
            data_dir="data/z6_data",
        ),
        PermutationGroupsConfig(
            name="d3_data",
            description="Dihedral Group D3 (order 6).",
            group_name="D3",
            group_degree=3,
            group_order=6,
            data_dir="data/d3_data",
        ),
        PermutationGroupsConfig(
            name="d4_data",
            description="Dihedral Group D4 (order 8).",
            group_name="D4",
            group_degree=4,
            group_order=8,
            data_dir="data/d4_data",
        ),
        PermutationGroupsConfig(
            name="d5_data",
            description="Dihedral Group D5 (order 10).",
            group_name="D5",
            group_degree=5,
            group_order=10,
            data_dir="data/d5_data",
        ),
        PermutationGroupsConfig(
            name="d6_data",
            description="Dihedral Group D6 (order 12).",
            group_name="D6",
            group_degree=6,
            group_order=12,
            data_dir="data/d6_data",
        ),
        PermutationGroupsConfig(
            name="d7_data",
            description="Dihedral Group D7 (order 14).",
            group_name="D7",
            group_degree=7,
            group_order=14,
            data_dir="data/d7_data",
        ),
        PermutationGroupsConfig(
            name="d8_data",
            description="Dihedral Group D8 (order 16).",
            group_name="D8",
            group_degree=8,
            group_order=16,
            data_dir="data/d8_data",
        ),
        PermutationGroupsConfig(
            name="psl25_data",
            description="PSL Group PSL25 (order 60).",
            group_name="PSL25",
            group_degree=6,
            group_order=60,
            data_dir="data/psl25_data",
        ),
        PermutationGroupsConfig(
            name="f20_data",
            description="Frobenius Group F20 (order 20).",
            group_name="F20",
            group_degree=5,
            group_order=20,
            data_dir="data/f20_data",
        ),
        PermutationGroupsConfig(
            name="s3_len10",
            description="Symmetric Group S3 (max_len=10).",
            group_name="S3",
            group_degree=3,
            group_order=6,
            data_dir="data/s3_data_len10",
            max_len=10,
        ),
        PermutationGroupsConfig(
            name="s4_len10",
            description="Symmetric Group S4 (max_len=10).",
            group_name="S4",
            group_degree=4,
            group_order=24,
            data_dir="data/s4_data_len10",
            max_len=10,
        ),
        PermutationGroupsConfig(
            name="s5_len10",
            description="Symmetric Group S5 (max_len=10).",
            group_name="S5",
            group_degree=5,
            group_order=120,
            data_dir="data/s5_data_len10",
            max_len=10,
        ),
        PermutationGroupsConfig(
            name="s6_len10",
            description="Symmetric Group S6 (max_len=10).",
            group_name="S6",
            group_degree=6,
            group_order=720,
            data_dir="data/s6_data_len10",
            max_len=10,
        ),
        PermutationGroupsConfig(
            name="s7_len10",
            description="Symmetric Group S7 (max_len=10).",
            group_name="S7",
            group_degree=7,
            group_order=5040,
            data_dir="data/s7_data_len10",
            max_len=10,
        ),
        PermutationGroupsConfig(
            name="a3_len10",
            description="Alternating Group A3 (max_len=10).",
            group_name="A3",
            group_degree=3,
            group_order=3,
            data_dir="data/a3_data_len10",
            max_len=10,
        ),
        PermutationGroupsConfig(
            name="a4_len10",
            description="Alternating Group A4 (max_len=10).",
            group_name="A4",
            group_degree=4,
            group_order=12,
            data_dir="data/a4_data_len10",
            max_len=10,
        ),
        PermutationGroupsConfig(
            name="a5_len10",
            description="Alternating Group A5 (max_len=10).",
            group_name="A5",
            group_degree=5,
            group_order=60,
            data_dir="data/a5_data_len10",
            max_len=10,
        ),
        PermutationGroupsConfig(
            name="a6_len10",
            description="Alternating Group A6 (max_len=10).",
            group_name="A6",
            group_degree=6,
            group_order=360,
            data_dir="data/a6_data_len10",
            max_len=10,
        ),
        PermutationGroupsConfig(
            name="a7_len10",
            description="Alternating Group A7 (max_len=10).",
            group_name="A7",
            group_degree=7,
            group_order=2520,
            data_dir="data/a7_data_len10",
            max_len=10,
        ),
        PermutationGroupsConfig(
            name="c3_len10",
            description="Cyclic Group C3 (max_len=10).",
            group_name="C3",
            group_degree=3,
            group_order=3,
            data_dir="data/c3_data_len10",
            max_len=10,
        ),
        PermutationGroupsConfig(
            name="c4_len10",
            description="Cyclic Group C4 (max_len=10).",
            group_name="C4",
            group_degree=4,
            group_order=4,
            data_dir="data/c4_data_len10",
            max_len=10,
        ),
        PermutationGroupsConfig(
            name="c5_len10",
            description="Cyclic Group C5 (max_len=10).",
            group_name="C5",
            group_degree=5,
            group_order=5,
            data_dir="data/c5_data_len10",
            max_len=10,
        ),
        PermutationGroupsConfig(
            name="c6_len10",
            description="Cyclic Group C6 (max_len=10).",
            group_name="C6",
            group_degree=6,
            group_order=6,
            data_dir="data/c6_data_len10",
            max_len=10,
        ),
        PermutationGroupsConfig(
            name="c7_len10",
            description="Cyclic Group C7 (max_len=10).",
            group_name="C7",
            group_degree=7,
            group_order=7,
            data_dir="data/c7_data_len10",
            max_len=10,
        ),
        PermutationGroupsConfig(
            name="c8_len10",
            description="Cyclic Group C8 (max_len=10).",
            group_name="C8",
            group_degree=8,
            group_order=8,
            data_dir="data/c8_data_len10",
            max_len=10,
        ),
        PermutationGroupsConfig(
            name="c10_len10",
            description="Cyclic Group C10 (max_len=10).",
            group_name="C10",
            group_degree=10,
            group_order=10,
            data_dir="data/c10_data_len10",
            max_len=10,
        ),
        PermutationGroupsConfig(
            name="c12_len10",
            description="Cyclic Group C12 (max_len=10).",
            group_name="C12",
            group_degree=12,
            group_order=12,
            data_dir="data/c12_data_len10",
            max_len=10,
        ),
        PermutationGroupsConfig(
            name="z3_len10",
            description="Cyclic Group Z3 (max_len=10).",
            group_name="Z3",
            group_degree=3,
            group_order=3,
            data_dir="data/z3_data_len10",
            max_len=10,
        ),
        PermutationGroupsConfig(
            name="z4_len10",
            description="Cyclic Group Z4 (max_len=10).",
            group_name="Z4",
            group_degree=4,
            group_order=4,
            data_dir="data/z4_data_len10",
            max_len=10,
        ),
        PermutationGroupsConfig(
            name="z5_len10",
            description="Cyclic Group Z5 (max_len=10).",
            group_name="Z5",
            group_degree=5,
            group_order=5,
            data_dir="data/z5_data_len10",
            max_len=10,
        ),
        PermutationGroupsConfig(
            name="z6_len10",
            description="Cyclic Group Z6 (max_len=10).",
            group_name="Z6",
            group_degree=6,
            group_order=6,
            data_dir="data/z6_data_len10",
            max_len=10,
        ),
        PermutationGroupsConfig(
            name="d3_len10",
            description="Dihedral Group D3 (max_len=10).",
            group_name="D3",
            group_degree=3,
            group_order=6,
            data_dir="data/d3_data_len10",
            max_len=10,
        ),
        PermutationGroupsConfig(
            name="d4_len10",
            description="Dihedral Group D4 (max_len=10).",
            group_name="D4",
            group_degree=4,
            group_order=8,
            data_dir="data/d4_data_len10",
            max_len=10,
        ),
        PermutationGroupsConfig(
            name="d5_len10",
            description="Dihedral Group D5 (max_len=10).",
            group_name="D5",
            group_degree=5,
            group_order=10,
            data_dir="data/d5_data_len10",
            max_len=10,
        ),
        PermutationGroupsConfig(
            name="d6_len10",
            description="Dihedral Group D6 (max_len=10).",
            group_name="D6",
            group_degree=6,
            group_order=12,
            data_dir="data/d6_data_len10",
            max_len=10,
        ),
        PermutationGroupsConfig(
            name="d7_len10",
            description="Dihedral Group D7 (max_len=10).",
            group_name="D7",
            group_degree=7,
            group_order=14,
            data_dir="data/d7_data_len10",
            max_len=10,
        ),
        PermutationGroupsConfig(
            name="d8_len10",
            description="Dihedral Group D8 (max_len=10).",
            group_name="D8",
            group_degree=8,
            group_order=16,
            data_dir="data/d8_data_len10",
            max_len=10,
        ),
        PermutationGroupsConfig(
            name="psl25_len10",
            description="PSL Group PSL25 (max_len=10).",
            group_name="PSL25",
            group_degree=6,
            group_order=60,
            data_dir="data/psl25_data_len10",
            max_len=10,
        ),
        PermutationGroupsConfig(
            name="f20_len10",
            description="Frobenius Group F20 (max_len=10).",
            group_name="F20",
            group_degree=5,
            group_order=20,
            data_dir="data/f20_data_len10",
            max_len=10,
        ),
        PermutationGroupsConfig(
            name="s3_len20",
            description="Symmetric Group S3 (max_len=20).",
            group_name="S3",
            group_degree=3,
            group_order=6,
            data_dir="data/s3_data_len20",
            max_len=20,
        ),
        PermutationGroupsConfig(
            name="s4_len20",
            description="Symmetric Group S4 (max_len=20).",
            group_name="S4",
            group_degree=4,
            group_order=24,
            data_dir="data/s4_data_len20",
            max_len=20,
        ),
        PermutationGroupsConfig(
            name="s5_len20",
            description="Symmetric Group S5 (max_len=20).",
            group_name="S5",
            group_degree=5,
            group_order=120,
            data_dir="data/s5_data_len20",
            max_len=20,
        ),
        PermutationGroupsConfig(
            name="s6_len20",
            description="Symmetric Group S6 (max_len=20).",
            group_name="S6",
            group_degree=6,
            group_order=720,
            data_dir="data/s6_data_len20",
            max_len=20,
        ),
        PermutationGroupsConfig(
            name="s7_len20",
            description="Symmetric Group S7 (max_len=20).",
            group_name="S7",
            group_degree=7,
            group_order=5040,
            data_dir="data/s7_data_len20",
            max_len=20,
        ),
        PermutationGroupsConfig(
            name="a3_len20",
            description="Alternating Group A3 (max_len=20).",
            group_name="A3",
            group_degree=3,
            group_order=3,
            data_dir="data/a3_data_len20",
            max_len=20,
        ),
        PermutationGroupsConfig(
            name="a4_len20",
            description="Alternating Group A4 (max_len=20).",
            group_name="A4",
            group_degree=4,
            group_order=12,
            data_dir="data/a4_data_len20",
            max_len=20,
        ),
        PermutationGroupsConfig(
            name="a5_len20",
            description="Alternating Group A5 (max_len=20).",
            group_name="A5",
            group_degree=5,
            group_order=60,
            data_dir="data/a5_data_len20",
            max_len=20,
        ),
        PermutationGroupsConfig(
            name="a6_len20",
            description="Alternating Group A6 (max_len=20).",
            group_name="A6",
            group_degree=6,
            group_order=360,
            data_dir="data/a6_data_len20",
            max_len=20,
        ),
        PermutationGroupsConfig(
            name="a7_len20",
            description="Alternating Group A7 (max_len=20).",
            group_name="A7",
            group_degree=7,
            group_order=2520,
            data_dir="data/a7_data_len20",
            max_len=20,
        ),
        PermutationGroupsConfig(
            name="c3_len20",
            description="Cyclic Group C3 (max_len=20).",
            group_name="C3",
            group_degree=3,
            group_order=3,
            data_dir="data/c3_data_len20",
            max_len=20,
        ),
        PermutationGroupsConfig(
            name="c4_len20",
            description="Cyclic Group C4 (max_len=20).",
            group_name="C4",
            group_degree=4,
            group_order=4,
            data_dir="data/c4_data_len20",
            max_len=20,
        ),
        PermutationGroupsConfig(
            name="c5_len20",
            description="Cyclic Group C5 (max_len=20).",
            group_name="C5",
            group_degree=5,
            group_order=5,
            data_dir="data/c5_data_len20",
            max_len=20,
        ),
        PermutationGroupsConfig(
            name="c6_len20",
            description="Cyclic Group C6 (max_len=20).",
            group_name="C6",
            group_degree=6,
            group_order=6,
            data_dir="data/c6_data_len20",
            max_len=20,
        ),
        PermutationGroupsConfig(
            name="c7_len20",
            description="Cyclic Group C7 (max_len=20).",
            group_name="C7",
            group_degree=7,
            group_order=7,
            data_dir="data/c7_data_len20",
            max_len=20,
        ),
        PermutationGroupsConfig(
            name="c8_len20",
            description="Cyclic Group C8 (max_len=20).",
            group_name="C8",
            group_degree=8,
            group_order=8,
            data_dir="data/c8_data_len20",
            max_len=20,
        ),
        PermutationGroupsConfig(
            name="c10_len20",
            description="Cyclic Group C10 (max_len=20).",
            group_name="C10",
            group_degree=10,
            group_order=10,
            data_dir="data/c10_data_len20",
            max_len=20,
        ),
        PermutationGroupsConfig(
            name="c12_len20",
            description="Cyclic Group C12 (max_len=20).",
            group_name="C12",
            group_degree=12,
            group_order=12,
            data_dir="data/c12_data_len20",
            max_len=20,
        ),
        PermutationGroupsConfig(
            name="z3_len20",
            description="Cyclic Group Z3 (max_len=20).",
            group_name="Z3",
            group_degree=3,
            group_order=3,
            data_dir="data/z3_data_len20",
            max_len=20,
        ),
        PermutationGroupsConfig(
            name="z4_len20",
            description="Cyclic Group Z4 (max_len=20).",
            group_name="Z4",
            group_degree=4,
            group_order=4,
            data_dir="data/z4_data_len20",
            max_len=20,
        ),
        PermutationGroupsConfig(
            name="z5_len20",
            description="Cyclic Group Z5 (max_len=20).",
            group_name="Z5",
            group_degree=5,
            group_order=5,
            data_dir="data/z5_data_len20",
            max_len=20,
        ),
        PermutationGroupsConfig(
            name="z6_len20",
            description="Cyclic Group Z6 (max_len=20).",
            group_name="Z6",
            group_degree=6,
            group_order=6,
            data_dir="data/z6_data_len20",
            max_len=20,
        ),
        PermutationGroupsConfig(
            name="d3_len20",
            description="Dihedral Group D3 (max_len=20).",
            group_name="D3",
            group_degree=3,
            group_order=6,
            data_dir="data/d3_data_len20",
            max_len=20,
        ),
        PermutationGroupsConfig(
            name="d4_len20",
            description="Dihedral Group D4 (max_len=20).",
            group_name="D4",
            group_degree=4,
            group_order=8,
            data_dir="data/d4_data_len20",
            max_len=20,
        ),
        PermutationGroupsConfig(
            name="d5_len20",
            description="Dihedral Group D5 (max_len=20).",
            group_name="D5",
            group_degree=5,
            group_order=10,
            data_dir="data/d5_data_len20",
            max_len=20,
        ),
        PermutationGroupsConfig(
            name="d6_len20",
            description="Dihedral Group D6 (max_len=20).",
            group_name="D6",
            group_degree=6,
            group_order=12,
            data_dir="data/d6_data_len20",
            max_len=20,
        ),
        PermutationGroupsConfig(
            name="d7_len20",
            description="Dihedral Group D7 (max_len=20).",
            group_name="D7",
            group_degree=7,
            group_order=14,
            data_dir="data/d7_data_len20",
            max_len=20,
        ),
        PermutationGroupsConfig(
            name="d8_len20",
            description="Dihedral Group D8 (max_len=20).",
            group_name="D8",
            group_degree=8,
            group_order=16,
            data_dir="data/d8_data_len20",
            max_len=20,
        ),
        PermutationGroupsConfig(
            name="psl25_len20",
            description="PSL Group PSL25 (max_len=20).",
            group_name="PSL25",
            group_degree=6,
            group_order=60,
            data_dir="data/psl25_data_len20",
            max_len=20,
        ),
        PermutationGroupsConfig(
            name="f20_len20",
            description="Frobenius Group F20 (max_len=20).",
            group_name="F20",
            group_degree=5,
            group_order=20,
            data_dir="data/f20_data_len20",
            max_len=20,
        ),
        PermutationGroupsConfig(
            name="s3_len30",
            description="Symmetric Group S3 (max_len=30).",
            group_name="S3",
            group_degree=3,
            group_order=6,
            data_dir="data/s3_data_len30",
            max_len=30,
        ),
        PermutationGroupsConfig(
            name="s4_len30",
            description="Symmetric Group S4 (max_len=30).",
            group_name="S4",
            group_degree=4,
            group_order=24,
            data_dir="data/s4_data_len30",
            max_len=30,
        ),
        PermutationGroupsConfig(
            name="s5_len30",
            description="Symmetric Group S5 (max_len=30).",
            group_name="S5",
            group_degree=5,
            group_order=120,
            data_dir="data/s5_data_len30",
            max_len=30,
        ),
        PermutationGroupsConfig(
            name="s6_len30",
            description="Symmetric Group S6 (max_len=30).",
            group_name="S6",
            group_degree=6,
            group_order=720,
            data_dir="data/s6_data_len30",
            max_len=30,
        ),
        PermutationGroupsConfig(
            name="s7_len30",
            description="Symmetric Group S7 (max_len=30).",
            group_name="S7",
            group_degree=7,
            group_order=5040,
            data_dir="data/s7_data_len30",
            max_len=30,
        ),
        PermutationGroupsConfig(
            name="a3_len30",
            description="Alternating Group A3 (max_len=30).",
            group_name="A3",
            group_degree=3,
            group_order=3,
            data_dir="data/a3_data_len30",
            max_len=30,
        ),
        PermutationGroupsConfig(
            name="a4_len30",
            description="Alternating Group A4 (max_len=30).",
            group_name="A4",
            group_degree=4,
            group_order=12,
            data_dir="data/a4_data_len30",
            max_len=30,
        ),
        PermutationGroupsConfig(
            name="a5_len30",
            description="Alternating Group A5 (max_len=30).",
            group_name="A5",
            group_degree=5,
            group_order=60,
            data_dir="data/a5_data_len30",
            max_len=30,
        ),
        PermutationGroupsConfig(
            name="a6_len30",
            description="Alternating Group A6 (max_len=30).",
            group_name="A6",
            group_degree=6,
            group_order=360,
            data_dir="data/a6_data_len30",
            max_len=30,
        ),
        PermutationGroupsConfig(
            name="a7_len30",
            description="Alternating Group A7 (max_len=30).",
            group_name="A7",
            group_degree=7,
            group_order=2520,
            data_dir="data/a7_data_len30",
            max_len=30,
        ),
        PermutationGroupsConfig(
            name="c3_len30",
            description="Cyclic Group C3 (max_len=30).",
            group_name="C3",
            group_degree=3,
            group_order=3,
            data_dir="data/c3_data_len30",
            max_len=30,
        ),
        PermutationGroupsConfig(
            name="c4_len30",
            description="Cyclic Group C4 (max_len=30).",
            group_name="C4",
            group_degree=4,
            group_order=4,
            data_dir="data/c4_data_len30",
            max_len=30,
        ),
        PermutationGroupsConfig(
            name="c5_len30",
            description="Cyclic Group C5 (max_len=30).",
            group_name="C5",
            group_degree=5,
            group_order=5,
            data_dir="data/c5_data_len30",
            max_len=30,
        ),
        PermutationGroupsConfig(
            name="c6_len30",
            description="Cyclic Group C6 (max_len=30).",
            group_name="C6",
            group_degree=6,
            group_order=6,
            data_dir="data/c6_data_len30",
            max_len=30,
        ),
        PermutationGroupsConfig(
            name="c7_len30",
            description="Cyclic Group C7 (max_len=30).",
            group_name="C7",
            group_degree=7,
            group_order=7,
            data_dir="data/c7_data_len30",
            max_len=30,
        ),
        PermutationGroupsConfig(
            name="c8_len30",
            description="Cyclic Group C8 (max_len=30).",
            group_name="C8",
            group_degree=8,
            group_order=8,
            data_dir="data/c8_data_len30",
            max_len=30,
        ),
        PermutationGroupsConfig(
            name="c10_len30",
            description="Cyclic Group C10 (max_len=30).",
            group_name="C10",
            group_degree=10,
            group_order=10,
            data_dir="data/c10_data_len30",
            max_len=30,
        ),
        PermutationGroupsConfig(
            name="c12_len30",
            description="Cyclic Group C12 (max_len=30).",
            group_name="C12",
            group_degree=12,
            group_order=12,
            data_dir="data/c12_data_len30",
            max_len=30,
        ),
        PermutationGroupsConfig(
            name="z3_len30",
            description="Cyclic Group Z3 (max_len=30).",
            group_name="Z3",
            group_degree=3,
            group_order=3,
            data_dir="data/z3_data_len30",
            max_len=30,
        ),
        PermutationGroupsConfig(
            name="z4_len30",
            description="Cyclic Group Z4 (max_len=30).",
            group_name="Z4",
            group_degree=4,
            group_order=4,
            data_dir="data/z4_data_len30",
            max_len=30,
        ),
        PermutationGroupsConfig(
            name="z5_len30",
            description="Cyclic Group Z5 (max_len=30).",
            group_name="Z5",
            group_degree=5,
            group_order=5,
            data_dir="data/z5_data_len30",
            max_len=30,
        ),
        PermutationGroupsConfig(
            name="z6_len30",
            description="Cyclic Group Z6 (max_len=30).",
            group_name="Z6",
            group_degree=6,
            group_order=6,
            data_dir="data/z6_data_len30",
            max_len=30,
        ),
        PermutationGroupsConfig(
            name="d3_len30",
            description="Dihedral Group D3 (max_len=30).",
            group_name="D3",
            group_degree=3,
            group_order=6,
            data_dir="data/d3_data_len30",
            max_len=30,
        ),
        PermutationGroupsConfig(
            name="d4_len30",
            description="Dihedral Group D4 (max_len=30).",
            group_name="D4",
            group_degree=4,
            group_order=8,
            data_dir="data/d4_data_len30",
            max_len=30,
        ),
        PermutationGroupsConfig(
            name="d5_len30",
            description="Dihedral Group D5 (max_len=30).",
            group_name="D5",
            group_degree=5,
            group_order=10,
            data_dir="data/d5_data_len30",
            max_len=30,
        ),
        PermutationGroupsConfig(
            name="d6_len30",
            description="Dihedral Group D6 (max_len=30).",
            group_name="D6",
            group_degree=6,
            group_order=12,
            data_dir="data/d6_data_len30",
            max_len=30,
        ),
        PermutationGroupsConfig(
            name="d7_len30",
            description="Dihedral Group D7 (max_len=30).",
            group_name="D7",
            group_degree=7,
            group_order=14,
            data_dir="data/d7_data_len30",
            max_len=30,
        ),
        PermutationGroupsConfig(
            name="d8_len30",
            description="Dihedral Group D8 (max_len=30).",
            group_name="D8",
            group_degree=8,
            group_order=16,
            data_dir="data/d8_data_len30",
            max_len=30,
        ),
        PermutationGroupsConfig(
            name="psl25_len30",
            description="PSL Group PSL25 (max_len=30).",
            group_name="PSL25",
            group_degree=6,
            group_order=60,
            data_dir="data/psl25_data_len30",
            max_len=30,
        ),
        PermutationGroupsConfig(
            name="f20_len30",
            description="Frobenius Group F20 (max_len=30).",
            group_name="F20",
            group_degree=5,
            group_order=20,
            data_dir="data/f20_data_len30",
            max_len=30,
        ),
        PermutationGroupsConfig(
            name="s3_len100",
            description="Symmetric Group S3 (max_len=100).",
            group_name="S3",
            group_degree=3,
            group_order=6,
            data_dir="data/s3_data_len100",
            max_len=100,
        ),
        PermutationGroupsConfig(
            name="s4_len100",
            description="Symmetric Group S4 (max_len=100).",
            group_name="S4",
            group_degree=4,
            group_order=24,
            data_dir="data/s4_data_len100",
            max_len=100,
        ),
        PermutationGroupsConfig(
            name="s5_len100",
            description="Symmetric Group S5 (max_len=100).",
            group_name="S5",
            group_degree=5,
            group_order=120,
            data_dir="data/s5_data_len100",
            max_len=100,
        ),
        PermutationGroupsConfig(
            name="s6_len100",
            description="Symmetric Group S6 (max_len=100).",
            group_name="S6",
            group_degree=6,
            group_order=720,
            data_dir="data/s6_data_len100",
            max_len=100,
        ),
        PermutationGroupsConfig(
            name="s7_len100",
            description="Symmetric Group S7 (max_len=100).",
            group_name="S7",
            group_degree=7,
            group_order=5040,
            data_dir="data/s7_data_len100",
            max_len=100,
        ),
        PermutationGroupsConfig(
            name="a3_len100",
            description="Alternating Group A3 (max_len=100).",
            group_name="A3",
            group_degree=3,
            group_order=3,
            data_dir="data/a3_data_len100",
            max_len=100,
        ),
        PermutationGroupsConfig(
            name="a4_len100",
            description="Alternating Group A4 (max_len=100).",
            group_name="A4",
            group_degree=4,
            group_order=12,
            data_dir="data/a4_data_len100",
            max_len=100,
        ),
        PermutationGroupsConfig(
            name="a5_len100",
            description="Alternating Group A5 (max_len=100).",
            group_name="A5",
            group_degree=5,
            group_order=60,
            data_dir="data/a5_data_len100",
            max_len=100,
        ),
        PermutationGroupsConfig(
            name="a6_len100",
            description="Alternating Group A6 (max_len=100).",
            group_name="A6",
            group_degree=6,
            group_order=360,
            data_dir="data/a6_data_len100",
            max_len=100,
        ),
        PermutationGroupsConfig(
            name="a7_len100",
            description="Alternating Group A7 (max_len=100).",
            group_name="A7",
            group_degree=7,
            group_order=2520,
            data_dir="data/a7_data_len100",
            max_len=100,
        ),
        PermutationGroupsConfig(
            name="c3_len100",
            description="Cyclic Group C3 (max_len=100).",
            group_name="C3",
            group_degree=3,
            group_order=3,
            data_dir="data/c3_data_len100",
            max_len=100,
        ),
        PermutationGroupsConfig(
            name="c4_len100",
            description="Cyclic Group C4 (max_len=100).",
            group_name="C4",
            group_degree=4,
            group_order=4,
            data_dir="data/c4_data_len100",
            max_len=100,
        ),
        PermutationGroupsConfig(
            name="c5_len100",
            description="Cyclic Group C5 (max_len=100).",
            group_name="C5",
            group_degree=5,
            group_order=5,
            data_dir="data/c5_data_len100",
            max_len=100,
        ),
        PermutationGroupsConfig(
            name="c6_len100",
            description="Cyclic Group C6 (max_len=100).",
            group_name="C6",
            group_degree=6,
            group_order=6,
            data_dir="data/c6_data_len100",
            max_len=100,
        ),
        PermutationGroupsConfig(
            name="c7_len100",
            description="Cyclic Group C7 (max_len=100).",
            group_name="C7",
            group_degree=7,
            group_order=7,
            data_dir="data/c7_data_len100",
            max_len=100,
        ),
        PermutationGroupsConfig(
            name="c8_len100",
            description="Cyclic Group C8 (max_len=100).",
            group_name="C8",
            group_degree=8,
            group_order=8,
            data_dir="data/c8_data_len100",
            max_len=100,
        ),
        PermutationGroupsConfig(
            name="c10_len100",
            description="Cyclic Group C10 (max_len=100).",
            group_name="C10",
            group_degree=10,
            group_order=10,
            data_dir="data/c10_data_len100",
            max_len=100,
        ),
        PermutationGroupsConfig(
            name="c12_len100",
            description="Cyclic Group C12 (max_len=100).",
            group_name="C12",
            group_degree=12,
            group_order=12,
            data_dir="data/c12_data_len100",
            max_len=100,
        ),
        PermutationGroupsConfig(
            name="z3_len100",
            description="Cyclic Group Z3 (max_len=100).",
            group_name="Z3",
            group_degree=3,
            group_order=3,
            data_dir="data/z3_data_len100",
            max_len=100,
        ),
        PermutationGroupsConfig(
            name="z4_len100",
            description="Cyclic Group Z4 (max_len=100).",
            group_name="Z4",
            group_degree=4,
            group_order=4,
            data_dir="data/z4_data_len100",
            max_len=100,
        ),
        PermutationGroupsConfig(
            name="z5_len100",
            description="Cyclic Group Z5 (max_len=100).",
            group_name="Z5",
            group_degree=5,
            group_order=5,
            data_dir="data/z5_data_len100",
            max_len=100,
        ),
        PermutationGroupsConfig(
            name="z6_len100",
            description="Cyclic Group Z6 (max_len=100).",
            group_name="Z6",
            group_degree=6,
            group_order=6,
            data_dir="data/z6_data_len100",
            max_len=100,
        ),
        PermutationGroupsConfig(
            name="d3_len100",
            description="Dihedral Group D3 (max_len=100).",
            group_name="D3",
            group_degree=3,
            group_order=6,
            data_dir="data/d3_data_len100",
            max_len=100,
        ),
        PermutationGroupsConfig(
            name="d4_len100",
            description="Dihedral Group D4 (max_len=100).",
            group_name="D4",
            group_degree=4,
            group_order=8,
            data_dir="data/d4_data_len100",
            max_len=100,
        ),
        PermutationGroupsConfig(
            name="d5_len100",
            description="Dihedral Group D5 (max_len=100).",
            group_name="D5",
            group_degree=5,
            group_order=10,
            data_dir="data/d5_data_len100",
            max_len=100,
        ),
        PermutationGroupsConfig(
            name="d6_len100",
            description="Dihedral Group D6 (max_len=100).",
            group_name="D6",
            group_degree=6,
            group_order=12,
            data_dir="data/d6_data_len100",
            max_len=100,
        ),
        PermutationGroupsConfig(
            name="d7_len100",
            description="Dihedral Group D7 (max_len=100).",
            group_name="D7",
            group_degree=7,
            group_order=14,
            data_dir="data/d7_data_len100",
            max_len=100,
        ),
        PermutationGroupsConfig(
            name="d8_len100",
            description="Dihedral Group D8 (max_len=100).",
            group_name="D8",
            group_degree=8,
            group_order=16,
            data_dir="data/d8_data_len100",
            max_len=100,
        ),
        PermutationGroupsConfig(
            name="psl25_len100",
            description="PSL Group PSL25 (max_len=100).",
            group_name="PSL25",
            group_degree=6,
            group_order=60,
            data_dir="data/psl25_data_len100",
            max_len=100,
        ),
        PermutationGroupsConfig(
            name="f20_len100",
            description="Frobenius Group F20 (max_len=100).",
            group_name="F20",
            group_degree=5,
            group_order=20,
            data_dir="data/f20_data_len100",
            max_len=100,
        ),
        PermutationGroupsConfig(
            name="s3_len512",
            description="Symmetric Group S3 (max_len=512).",
            group_name="S3",
            group_degree=3,
            group_order=6,
            data_dir="data/s3_data_len512",
            max_len=512,
        ),
        PermutationGroupsConfig(
            name="s4_len512",
            description="Symmetric Group S4 (max_len=512).",
            group_name="S4",
            group_degree=4,
            group_order=24,
            data_dir="data/s4_data_len512",
            max_len=512,
        ),
        PermutationGroupsConfig(
            name="s5_len512",
            description="Symmetric Group S5 (max_len=512).",
            group_name="S5",
            group_degree=5,
            group_order=120,
            data_dir="data/s5_data_len512",
            max_len=512,
        ),
        PermutationGroupsConfig(
            name="s6_len512",
            description="Symmetric Group S6 (max_len=512).",
            group_name="S6",
            group_degree=6,
            group_order=720,
            data_dir="data/s6_data_len512",
            max_len=512,
        ),
        PermutationGroupsConfig(
            name="s7_len512",
            description="Symmetric Group S7 (max_len=512).",
            group_name="S7",
            group_degree=7,
            group_order=5040,
            data_dir="data/s7_data_len512",
            max_len=512,
        ),
        PermutationGroupsConfig(
            name="a3_len512",
            description="Alternating Group A3 (max_len=512).",
            group_name="A3",
            group_degree=3,
            group_order=3,
            data_dir="data/a3_data_len512",
            max_len=512,
        ),
        PermutationGroupsConfig(
            name="a4_len512",
            description="Alternating Group A4 (max_len=512).",
            group_name="A4",
            group_degree=4,
            group_order=12,
            data_dir="data/a4_data_len512",
            max_len=512,
        ),
        PermutationGroupsConfig(
            name="a5_len512",
            description="Alternating Group A5 (max_len=512).",
            group_name="A5",
            group_degree=5,
            group_order=60,
            data_dir="data/a5_data_len512",
            max_len=512,
        ),
        PermutationGroupsConfig(
            name="a6_len512",
            description="Alternating Group A6 (max_len=512).",
            group_name="A6",
            group_degree=6,
            group_order=360,
            data_dir="data/a6_data_len512",
            max_len=512,
        ),
        PermutationGroupsConfig(
            name="a7_len512",
            description="Alternating Group A7 (max_len=512).",
            group_name="A7",
            group_degree=7,
            group_order=2520,
            data_dir="data/a7_data_len512",
            max_len=512,
        ),
        PermutationGroupsConfig(
            name="c3_len512",
            description="Cyclic Group C3 (max_len=512).",
            group_name="C3",
            group_degree=3,
            group_order=3,
            data_dir="data/c3_data_len512",
            max_len=512,
        ),
        PermutationGroupsConfig(
            name="c4_len512",
            description="Cyclic Group C4 (max_len=512).",
            group_name="C4",
            group_degree=4,
            group_order=4,
            data_dir="data/c4_data_len512",
            max_len=512,
        ),
        PermutationGroupsConfig(
            name="c5_len512",
            description="Cyclic Group C5 (max_len=512).",
            group_name="C5",
            group_degree=5,
            group_order=5,
            data_dir="data/c5_data_len512",
            max_len=512,
        ),
        PermutationGroupsConfig(
            name="c6_len512",
            description="Cyclic Group C6 (max_len=512).",
            group_name="C6",
            group_degree=6,
            group_order=6,
            data_dir="data/c6_data_len512",
            max_len=512,
        ),
        PermutationGroupsConfig(
            name="c7_len512",
            description="Cyclic Group C7 (max_len=512).",
            group_name="C7",
            group_degree=7,
            group_order=7,
            data_dir="data/c7_data_len512",
            max_len=512,
        ),
        PermutationGroupsConfig(
            name="c8_len512",
            description="Cyclic Group C8 (max_len=512).",
            group_name="C8",
            group_degree=8,
            group_order=8,
            data_dir="data/c8_data_len512",
            max_len=512,
        ),
        PermutationGroupsConfig(
            name="c10_len512",
            description="Cyclic Group C10 (max_len=512).",
            group_name="C10",
            group_degree=10,
            group_order=10,
            data_dir="data/c10_data_len512",
            max_len=512,
        ),
        PermutationGroupsConfig(
            name="c12_len512",
            description="Cyclic Group C12 (max_len=512).",
            group_name="C12",
            group_degree=12,
            group_order=12,
            data_dir="data/c12_data_len512",
            max_len=512,
        ),
        PermutationGroupsConfig(
            name="z3_len512",
            description="Cyclic Group Z3 (max_len=512).",
            group_name="Z3",
            group_degree=3,
            group_order=3,
            data_dir="data/z3_data_len512",
            max_len=512,
        ),
        PermutationGroupsConfig(
            name="z4_len512",
            description="Cyclic Group Z4 (max_len=512).",
            group_name="Z4",
            group_degree=4,
            group_order=4,
            data_dir="data/z4_data_len512",
            max_len=512,
        ),
        PermutationGroupsConfig(
            name="z5_len512",
            description="Cyclic Group Z5 (max_len=512).",
            group_name="Z5",
            group_degree=5,
            group_order=5,
            data_dir="data/z5_data_len512",
            max_len=512,
        ),
        PermutationGroupsConfig(
            name="z6_len512",
            description="Cyclic Group Z6 (max_len=512).",
            group_name="Z6",
            group_degree=6,
            group_order=6,
            data_dir="data/z6_data_len512",
            max_len=512,
        ),
        PermutationGroupsConfig(
            name="d3_len512",
            description="Dihedral Group D3 (max_len=512).",
            group_name="D3",
            group_degree=3,
            group_order=6,
            data_dir="data/d3_data_len512",
            max_len=512,
        ),
        PermutationGroupsConfig(
            name="d4_len512",
            description="Dihedral Group D4 (max_len=512).",
            group_name="D4",
            group_degree=4,
            group_order=8,
            data_dir="data/d4_data_len512",
            max_len=512,
        ),
        PermutationGroupsConfig(
            name="d5_len512",
            description="Dihedral Group D5 (max_len=512).",
            group_name="D5",
            group_degree=5,
            group_order=10,
            data_dir="data/d5_data_len512",
            max_len=512,
        ),
        PermutationGroupsConfig(
            name="d6_len512",
            description="Dihedral Group D6 (max_len=512).",
            group_name="D6",
            group_degree=6,
            group_order=12,
            data_dir="data/d6_data_len512",
            max_len=512,
        ),
        PermutationGroupsConfig(
            name="d7_len512",
            description="Dihedral Group D7 (max_len=512).",
            group_name="D7",
            group_degree=7,
            group_order=14,
            data_dir="data/d7_data_len512",
            max_len=512,
        ),
        PermutationGroupsConfig(
            name="d8_len512",
            description="Dihedral Group D8 (max_len=512).",
            group_name="D8",
            group_degree=8,
            group_order=16,
            data_dir="data/d8_data_len512",
            max_len=512,
        ),
        PermutationGroupsConfig(
            name="psl25_len512",
            description="PSL Group PSL25 (max_len=512).",
            group_name="PSL25",
            group_degree=6,
            group_order=60,
            data_dir="data/psl25_data_len512",
            max_len=512,
        ),
        PermutationGroupsConfig(
            name="f20_len512",
            description="Frobenius Group F20 (max_len=512).",
            group_name="F20",
            group_degree=5,
            group_order=20,
            data_dir="data/f20_data_len512",
            max_len=512,
        ),
        PermutationGroupsConfig(
            name="all",
            description="All Permutation Composition Datasets.",
            group_name="All",
            group_degree=None,
            group_order=None,
            data_dir=None,
        ),
        PermutationGroupsConfig(
            name="all_len10",
            description="All Groups (max_len=10).",
            group_name="All",
            group_degree=None,
            group_order=None,
            data_dir=None,
            max_len=10,
        ),
        PermutationGroupsConfig(
            name="all_len20",
            description="All Groups (max_len=20).",
            group_name="All",
            group_degree=None,
            group_order=None,
            data_dir=None,
            max_len=20,
        ),
        PermutationGroupsConfig(
            name="all_len30",
            description="All Groups (max_len=30).",
            group_name="All",
            group_degree=None,
            group_order=None,
            data_dir=None,
            max_len=30,
        ),
        PermutationGroupsConfig(
            name="all_len100",
            description="All Groups (max_len=100).",
            group_name="All",
            group_degree=None,
            group_order=None,
            data_dir=None,
            max_len=100,
        ),
        PermutationGroupsConfig(
            name="all_len512",
            description="All Groups (max_len=512).",
            group_name="All",
            group_degree=None,
            group_order=None,
            data_dir=None,
            max_len=512,
        ),
    ]

    DEFAULT_CONFIG_NAME = "s5_data"

    def _info(self):
        return datasets.DatasetInfo(
            description=_DESCRIPTION,
            features=datasets.Features({
                "input_sequence": datasets.Value("string"),
                "target": datasets.Value("string"),
            }),
            homepage=_HOMEPAGE,
            license=_LICENSE,
        )

    def _split_generators(self, dl_manager):
        # Handle the "all" configurations
        if self.config.name.startswith("all"):
            # Determine which groups to include
            if self.config.name == "all":
                # Original all - just the base configs
                all_configs = [f"{g.lower()}_data" for g in ['S3', 'S4', 'S5', 'S6', 'S7', 'A3', 'A4', 'A5', 'A6', 'A7', 'C3', 'C4', 'C5', 'C6', 'C7', 'C8', 'C10', 'C12', 'Z3', 'Z4', 'Z5', 'Z6', 'D3', 'D4', 'D5', 'D6', 'D7', 'D8', 'PSL25', 'F20']]
            else:
                # Length-specific all
                length = self.config.max_len
                all_configs = [f"{g.lower()}_len{length}" for g in ['S3', 'S4', 'S5', 'S6', 'S7', 'A3', 'A4', 'A5', 'A6', 'A7', 'C3', 'C4', 'C5', 'C6', 'C7', 'C8', 'C10', 'C12', 'Z3', 'Z4', 'Z5', 'Z6', 'D3', 'D4', 'D5', 'D6', 'D7', 'D8', 'PSL25', 'F20']]
            
            # Download all arrow files
            train_files = []
            test_files = []
            
            for config in all_configs:
                data_urls = {
                    "train": f"data/{config}/train/data-00000-of-00001.arrow",
                    "test": f"data/{config}/test/data-00000-of-00001.arrow",
                }
                try:
                    downloaded = dl_manager.download(data_urls)
                    train_files.append(downloaded["train"])
                    test_files.append(downloaded["test"])
                except:
                    # Skip if dataset doesn't exist
                    pass
            
            return [
                datasets.SplitGenerator(
                    name=datasets.Split.TRAIN,
                    gen_kwargs={
                        "files": train_files,
                    },
                ),
                datasets.SplitGenerator(
                    name=datasets.Split.TEST,
                    gen_kwargs={
                        "files": test_files,
                    },
                ),
            ]
        else:
            # Single configuration
            data_urls = {
                "train": [f"{self.config.data_dir}/train/data-00000-of-00001.arrow"],
                "test": [f"{self.config.data_dir}/test/data-00000-of-00001.arrow"],
            }
            
            downloaded_files = dl_manager.download(data_urls)
            
            return [
                datasets.SplitGenerator(
                    name=datasets.Split.TRAIN,
                    gen_kwargs={
                        "files": downloaded_files["train"],
                    },
                ),
                datasets.SplitGenerator(
                    name=datasets.Split.TEST,
                    gen_kwargs={
                        "files": downloaded_files["test"],
                    },
                ),
            ]

    def _generate_tables(self, files):
        """Yield arrow tables directly for better performance."""
        for file_idx, file in enumerate(files):
            # Load the dataset using the datasets library format
            dataset = datasets.Dataset.from_file(file)
            # Get the underlying Arrow table
            table = dataset.data.table
            yield file_idx, table