table A13.2partmod7.pdf  sha256 96effe4c1c0e37bebba2daa2f1f001f02b539000f89dcb3808aad548b426e6bd
S_13 mod 7; pypdf 6.16.2
self-test of the Murnaghan-Nakayama code (hook formula, row orthogonality) for S_13: True
pages: 21, sections: 21; row blocks: 3; column blocks: 7
title line: 'A13.2 (mod 7)'
partitions of 13: 101; rows found: 101; columns: 90; distinct label strings among the partitions: 100
parse problems: 0
r-regular partitions: 90; columns = r-regular partitions with unitriangular block (James): True
r-regular classes: 90 (must equal the number of columns: True)
M B = X on all 101 rows x 90 classes: inconsistent pairs = 0; degrees positive: True
block check (nonzero decomposition numbers only between partitions with the same 7-core): violations = 0; blocks: 35, of defect zero (7-cores of size 13): 24
columns with a single nonzero entry: 24; single +1 alterations invisible to M B = X (and to unitriangularity and positive degrees): 840; all of them violate the block check
13-cycle: fixed-space dimensions integral and >= 0: True; fixed-point-free on 2 simple module(s): ϕ3 = D^(12, 1) dim 12 [N]; ϕ4 = D^(2, 2, 2, 2, 2, 2, 1) dim 12 [N(x)sgn]; max |beta(x)| = 1
  list is exactly {N, N (x) sgn}: True
11-cycle: fixed-space dimensions integral and >= 0: True; fixed-point-free on 0 simple module(s): none; max |beta(x)| = 1
negative controls: entry (1761, ϕ1) + 1 -> 90 inconsistent pairs; entry (1352, ϕ1) + 1 -> 0 inconsistent pairs
