table A17.2partmod13.pdf  sha256 6dfeba57f27e20feef40c053598eccd4a9ea7ee2af551bae6a90d20b5671dae9
S_17 mod 13; pypdf 6.16.2
pages: 158, sections: 168; row blocks: 8; column blocks: 21
title line: 'A17.2 (mod 13)'
partitions of 17: 297; rows found: 297; columns: 292; distinct label strings among the partitions: 296
parse problems: 0
r-regular partitions: 292; columns = r-regular partitions with unitriangular block (James): True
r-regular classes: 292 (must equal the number of columns: True)
M B = X on all 297 rows x 292 classes: inconsistent pairs = 0; degrees positive: True
block check (nonzero decomposition numbers only between partitions with the same 13-core): violations = 0; blocks: 237, of defect zero (13-cores of size 17): 232
columns with a single nonzero entry: 232; single +1 alterations invisible to M B = X (and to unitriangularity and positive degrees): 20830; all of them violate the block check
17-cycle: fixed-space dimensions integral and >= 0: True; fixed-point-free on 2 simple module(s): ϕ3 = D^(16, 1) dim 16 [N]; ϕ4 = D^(2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1) dim 16 [N(x)sgn]; max |beta(x)| = 1
  list is exactly {N, N (x) sgn}: True
negative controls: entry (11341, ϕ1) + 1 -> 292 inconsistent pairs; entry (13315161, ϕ1) + 1 -> 0 inconsistent pairs
