table A13.2partmod3.pdf  sha256 9599b3526ee1d048418c46304f26dad13937841ed38912777ba6a5b4b081244d
S_13 mod 3; pypdf 6.16.2
self-test of the Murnaghan-Nakayama code (hook formula, row orthogonality) for S_13: True
pages: 12, sections: 12; row blocks: 3; column blocks: 4
title line: 'A13.2 (mod 3)'
partitions of 13: 101; rows found: 101; columns: 44; distinct label strings among the partitions: 100
parse problems: 0
r-regular partitions: 44; columns = r-regular partitions with unitriangular block (James): True
r-regular classes: 44 (must equal the number of columns: True)
M B = X on all 101 rows x 44 classes: inconsistent pairs = 0; degrees positive: True
block check (nonzero decomposition numbers only between partitions with the same 3-core): violations = 0; blocks: 5, of defect zero (3-cores of size 13): 0
columns with a single nonzero entry: 0; single +1 alterations invisible to M B = X (and to unitriangularity and positive degrees): 0; 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^(6, 6, 1) dim 12 [N(x)sgn]; max |beta(x)| = 2
  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)| = 2
negative controls: entry (13101, ϕ1) + 1 -> 44 inconsistent pairs; entry (1162, ϕ1) + 1 -> 308 inconsistent pairs
