Update README to reflect variable sequence lengths (3-1024)

README.md

@@ -642,35 +642,35 @@ Each example contains the following fields:
 
 ```python
 {
-    'input_sequence': "123 456 789 ... (1024 IDs)",  # Space-separated permutation IDs (fixed length 1024)
+    'input_sequence': "123 456 789 ...",             # Space-separated permutation IDs (variable length)
     'target': "234",                                  # Result of composition as string
-    'sequence_length': 1024,                          # Always 1024 (fixed length sequences)
+    'sequence_length': 512,                           # Length of input sequence (varies from 3 to 1024)
     'group_degree': 7,                                # Degree of the permutation group (e.g., S7 acts on 7 elements)
     'group_order': 5040,                              # Order (size) of the group (e.g., |S7| = 7!)
     'group_type': "symmetric"                         # Type of the group
 }
 ```
 
-Note: All sequences contain exactly 1024 permutation IDs. The provided target is the composition of all 1024 permutations. Researchers who need shorter sequences can take a subset of the permutation IDs and recompute the composition target for that subset.
+Note: Sequences contain a variable number of permutation IDs (uniformly distributed between 3 and 1024). The provided target is the composition of all permutations in the input sequence.
 
 ### Working with Different Sequence Lengths
 
-To work with sequences shorter than 1024, take a subset of permutation IDs and compute their composition:
+The dataset already contains sequences of varying lengths (3 to 1024). You can filter or analyze based on sequence length:
 
 ```python
 # Load full dataset
 dataset = load_dataset("BeeGass/Group-Theory-Collection", name="s5")
 
-# Example: Work with sequences of length 32
-example = dataset['train'][0]
-all_ids = example['input_sequence'].split()  # All 1024 permutation IDs
+# Example: Filter for specific sequence lengths
+short_sequences = dataset['train'].filter(lambda x: x['sequence_length'] <= 32)
+medium_sequences = dataset['train'].filter(lambda x: 32 < x['sequence_length'] <= 256)
+long_sequences = dataset['train'].filter(lambda x: x['sequence_length'] > 256)
 
-# Take first 32 permutation IDs
-subset_ids = all_ids[:32]
-
-# You would need to recompute the target for this subset
-# The new target would be the composition of these 32 permutations
-# (Implementation depends on your permutation representation)
+# Analyze sequence length distribution
+import numpy as np
+lengths = np.array(dataset['train']['sequence_length'])
+print(f"Min length: {lengths.min()}, Max length: {lengths.max()}")
+print(f"Mean length: {lengths.mean():.1f}, Std: {lengths.std():.1f}")
 ```
 
 ## Group Inventory