table A11.2partmod3.pdf  sha256 d6ae9b7e61f8992293366503979c74e78e50da0cc2a81bb024c77bcb518db9e5
S_11 mod 3; pypdf 6.16.2
self-test of the Murnaghan-Nakayama code (hook formula, row orthogonality) for S_11: True
pages: 3, sections: 4; row blocks: 2; column blocks: 2
title line: 'S11 (mod 3)'
partitions of 11: 56; rows found: 56; columns: 27; distinct label strings among the partitions: 55
parse problems: 0
r-regular partitions: 27; columns = r-regular partitions with unitriangular block (James): True
r-regular classes: 27 (must equal the number of columns: True)
M B = X on all 56 rows x 27 classes: inconsistent pairs = 0; degrees positive: True
block check (nonzero decomposition numbers only between partitions with the same 3-core): violations = 0; blocks: 4, of defect zero (3-cores of size 11): 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
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^(5, 5, 1) dim 10 [N(x)sgn]; max |beta(x)| = 1
  list is exactly {N, N (x) sgn}: True
negative controls: entry (1381, ϕ1) + 1 -> 27 inconsistent pairs; entry (123161, ϕ3) + 1 -> 63 inconsistent pairs
