table A13.2partmod5.pdf  sha256 8121dc6776bc1cf857511f7b21dd789ac1b568395d7fd389e2b271cd857fd96f
S_13 mod 5; pypdf 6.16.2
self-test of the Murnaghan-Nakayama code (hook formula, row orthogonality) for S_13: True
pages: 18, sections: 18; row blocks: 3; column blocks: 6
title line: 'A13.2 (mod 5)'
partitions of 13: 101; rows found: 101; columns: 76; distinct label strings among the partitions: 100
parse problems: 0
r-regular partitions: 76; columns = r-regular partitions with unitriangular block (James): True
r-regular classes: 76 (must equal the number of columns: True)
M B = X on all 101 rows x 76 classes: inconsistent pairs = 0; degrees positive: True
block check (nonzero decomposition numbers only between partitions with the same 5-core): violations = 0; blocks: 16, of defect zero (5-cores of size 13): 6
columns with a single nonzero entry: 6; single +1 alterations invisible to M B = X (and to unitriangularity and positive degrees): 233; 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^(3, 3, 3, 3, 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)| = 3
negative controls: entry (1581, ϕ1) + 1 -> 76 inconsistent pairs; entry (112361, ϕ1) + 1 -> 228 inconsistent pairs
