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README.md

@@ -6,7 +6,7 @@ tags:
   - symmetric-groups
   - representation-theory
   - gpu-computation
-pretty_name: Kronecker Coefficients (S_20 and S_30)
+pretty_name: "Kronecker Coefficients (S_20 and S_30)"
 size_categories:
   - 1B<n<10B
 ---
@@ -14,7 +14,7 @@ size_categories:
 # Kronecker Coefficients
 
 Complete Kronecker coefficient tables g(lambda, mu, nu) for S_20 and S_30.
-Computed on NVIDIA B200 GPU. **Largest ever published.**
+Computed on NVIDIA B200 GPU. To our knowledge, the largest such computation published.
 
 | n | Partitions | Nonzero triples | Max g | GPU time |
 |---|-----------|----------------|-------|----------|
@@ -23,37 +23,80 @@ Computed on NVIDIA B200 GPU. **Largest ever published.**
 
 ## Files
 
-### S_20 (complete)
-- `s20/kronecker_n20_full_tensor.npz` — Full 627x627x627 tensor (462 MB, numpy compressed)
-- `s20/kronecker_n20_nonzero.csv` — All nonzero g(i,j,k) as CSV (503 MB)
-- `s20/char_table_n20.bin` — Character table (int64, row-major, 627x627)
-- `s20/z_inv_n20.bin` — Inverse centralizer orders (float64, 627 entries)
-- `s20/partitions_n20.txt` — Partition index mapping
-
-### S_30 (character tables — recompute triples in 7 min on B200)
-- `s30/char_table_n30.bin` — Character table (int64, row-major, 5604x5604, 240 MB)
-- `s30/z_inv_n30.bin` — Inverse centralizer orders (float64, 5604 entries)
-- `s30/partitions_n30.txt` — Partition index mapping
-
-The full S_30 nonzero data (26.4B entries) is ~370 GB and not uploaded directly.
-With the character table and z_inv, anyone can recompute all Kronecker triples:
-
-
-
-Or use our CUDA kernel for GPU acceleration (7.4 min on B200).
+### S_5
+- `s5/partitions_n5.txt` -- Partition index mapping
+
+### S_20 (complete -- full tensor + nonzero list)
+- `s20/kronecker_n20_full_tensor.npz` -- Full 627x627x627 tensor (462 MB, numpy compressed)
+- `s20/kronecker_n20_nonzero.csv` -- All nonzero g(i,j,k) as CSV (503 MB)
+- `s20/char_table_n20.bin` -- Character table (int64, row-major, 627x627)
+- `s20/z_inv_n20.bin` -- Inverse centralizer orders (float64, 627 entries)
+- `s20/partitions_n20.txt` -- Partition index mapping
+
+### S_30 (complete -- 370 GB of nonzero triples + character tables)
+- `s30/nonzero/part_00000.bin` through `part_00011.bin` -- All 26.4B nonzero (i,j,k,g) tuples (370 GB total)
+  - Format: repeating (uint16 i, uint16 j, uint16 k, int64 g) = 14 bytes per record
+  - i <= j <= k (upper triangle only)
+- `s30/char_table_n30.bin` -- Character table (int64, row-major, 5604x5604, 240 MB)
+- `s30/z_inv_n30.bin` -- Inverse centralizer orders (float64, 5604 entries)
+- `s30/partitions_n30.txt` -- Partition index mapping
+
+## Reading the Binary Data
+
+```python
+import struct
+import numpy as np
+
+# Read S_30 nonzero triples from a binary part
+with open("part_00000.bin", "rb") as f:
+    while True:
+        buf = f.read(14)
+        if len(buf) < 14:
+            break
+        i, j, k = struct.unpack("HHH", buf[:6])
+        g = struct.unpack("q", buf[6:14])[0]
+        # i, j, k are partition indices (see partitions_n30.txt)
+        # g = Kronecker coefficient g(lambda_i, lambda_j, lambda_k)
+```
+
+## Recompute from Character Tables
+
+Anyone can recompute all Kronecker triples from the character tables:
+
+```python
+import numpy as np
+n = 20
+ct = np.fromfile("s20/char_table_n20.bin", dtype=np.int64).reshape(627, 627)
+zi = np.fromfile("s20/z_inv_n20.bin", dtype=np.float64)
+g = np.einsum("ic,jc,kc,c->ijk", ct.astype(float), ct.astype(float), ct.astype(float), zi)
+g = np.round(g).astype(np.int64)
+print(f"g((20),(20),(20)) = {g[0,0,0]}")  # 1
+```
+
+For S_30, the full tensor doesn't fit in RAM (1.4 TB). Use the CUDA kernel for slab-by-slab computation (7.4 min on B200).
 
 ## Method
 1. Character table via Murnaghan-Nakayama rule (rim-path method, CPU)
 2. Kronecker triple-sum via pure CUDA kernel (GPU, atomic reduction)
 
-Validated: row/column orthogonality for S_5 through S_12. dim sum = n!.
-
-## Quick Start
-
-
+Validated: row/column orthogonality for S_5 through S_12. Dimension sum = n!.
 
 ## Source
 - Code: [github.com/cahlen/idontknow](https://github.com/cahlen/idontknow)
 - Finding: [bigcompute.science/findings/kronecker-s30-largest-computation](https://bigcompute.science/findings/kronecker-s30-largest-computation/)
+- Website: [bigcompute.science](https://bigcompute.science)
+
+## Citation
+
+```bibtex
+@dataset{humphreys2026kronecker,
+  title   = {Kronecker Coefficients for S_20 and S_30},
+  author  = {Humphreys, Cahlen},
+  year    = {2026},
+  publisher = {Hugging Face},
+  url     = {https://huggingface.co/datasets/cahlen/kronecker-coefficients},
+  note    = {26.4 billion nonzero triples for S_30, NVIDIA B200}
+}
+```
 
 Human-AI collaborative work (Cahlen Humphreys + Claude). Not peer-reviewed. CC BY 4.0.