table A11.2partmod7.pdf  sha256 9267033d4ed3e309d123bfbf65f31f9f05178c2c0772b87b8631142d99fb3d48
S_11 mod 7; 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 7)'
partitions of 11: 56; rows found: 56; columns: 51; distinct label strings among the partitions: 55
parse problems: 0
r-regular partitions: 51; columns = r-regular partitions with unitriangular block (James): True
r-regular classes: 51 (must equal the number of columns: True)
M B = X on all 56 rows x 51 classes: inconsistent pairs = 0; degrees positive: True
block check (nonzero decomposition numbers only between partitions with the same 7-core): violations = 0; blocks: 26, of defect zero (7-cores of size 11): 21
columns with a single nonzero entry: 21; single +1 alterations invisible to M B = X (and to unitriangularity and positive degrees): 387; 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^(2, 2, 2, 2, 1, 1, 1) dim 10 [N(x)sgn]; max |beta(x)| = 1
  list is exactly {N, N (x) sgn}: True
negative controls: entry (1741, ϕ1) + 1 -> 51 inconsistent pairs; entry (2351, ϕ1) + 1 -> 51 inconsistent pairs
