table A13.2partmod2.pdf  sha256 58a4e454f90d927cb93483271b7019e289d5ea2eff44a84ff4ed2d2ad9d7a7db
S_13 mod 2; pypdf 6.16.2
self-test of the Murnaghan-Nakayama code (hook formula, row orthogonality) for S_13: True
pages: 6, sections: 6; row blocks: 3; column blocks: 2
title line: 'A13.2 (mod 2)'
partitions of 13: 101; rows found: 101; columns: 18; distinct label strings among the partitions: 100
parse problems: 0
r-regular partitions: 18; columns = r-regular partitions with unitriangular block (James): True
r-regular classes: 18 (must equal the number of columns: True)
M B = X on all 101 rows x 18 classes: inconsistent pairs = 0; degrees positive: True
block check (nonzero decomposition numbers only between partitions with the same 2-core): violations = 0; blocks: 2, of defect zero (2-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 1 simple module(s): ϕ2 = D^(12, 1) dim 12 [N]; max |beta(x)| = 2
  list is exactly {N} (r = 2, where N (x) sgn = N): True
11-cycle: fixed-space dimensions integral and >= 0: True; fixed-point-free on 0 simple module(s): none; max |beta(x)| = 3
negative controls: entry (12111, ϕ1) + 1 -> 18 inconsistent pairs; entry (213181, ϕ1) + 1 -> 234 inconsistent pairs
