table A18.2partmod3.pdf  sha256 6fc588972ae2e90d384c563e8119e7d35f519f9405a3f5ce93cf75a5d355cdb3
S_18 mod 3; pypdf 6.16.2
pages: 100, sections: 100; row blocks: 10; column blocks: 10
title line: 'A18.2 (mod 3)'
partitions of 18: 385; rows found: 385; columns: 135; distinct label strings among the partitions: 384
parse problems: 0
r-regular partitions: 135; columns = r-regular partitions with unitriangular block (James): True
r-regular classes: 135 (must equal the number of columns: True)
M B = X on all 385 rows x 135 classes: inconsistent pairs = 0; degrees positive: True
block check (nonzero decomposition numbers only between partitions with the same 3-core): violations = 0; blocks: 7, of defect zero (3-cores of size 18): 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
17-cycle: fixed-space dimensions integral and >= 0: True; fixed-point-free on 2 simple module(s): ϕ2 = D^(17, 1) dim 16 [OTHER]; ϕ46 = D^(9, 8, 1) dim 16 [OTHER]; max |beta(x)| = 3
  list is exactly {N, N (x) sgn}: False
negative controls: entry (13151, ϕ1) + 1 -> 135 inconsistent pairs; entry (12216181, ϕ3) + 1 -> 3390 inconsistent pairs
