table A11.2partmod5.pdf  sha256 6f17ca3b15279173644b9b098898151d1faae9edfe8b6da5113926b91f6ebfde
S_11 mod 5; pypdf 6.16.2
self-test of the Murnaghan-Nakayama code (hook formula, row orthogonality) for S_11: True
pages: 6, sections: 8; row blocks: 2; column blocks: 4
title line: 'S11 (mod 5)'
partitions of 11: 56; rows found: 56; columns: 44; distinct label strings among the partitions: 55
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 56 rows x 44 classes: inconsistent pairs = 0; degrees positive: True
block check (nonzero decomposition numbers only between partitions with the same 5-core): violations = 0; blocks: 13, of defect zero (5-cores of size 11): 6
columns with a single nonzero entry: 6; single +1 alterations invisible to M B = X (and to unitriangularity and positive degrees): 125; all of them violate the block check
11-cycle: fixed-space dimensions integral and >= 0: True; fixed-point-free on 2 simple module(s): ϕ3 = D^(10, 1) dim 10 [N]; ϕ4 = D^(3, 3, 2, 2, 1) dim 10 [N(x)sgn]; max |beta(x)| = 2
  list is exactly {N, N (x) sgn}: True
negative controls: entry (1561, ϕ1) + 1 -> 44 inconsistent pairs; entry (11213151, ϕ1) + 1 -> 44 inconsistent pairs
