table A17.2partmod7.pdf  sha256 49d0c35916406778aef0d5056a55c7b176e4dde9bb8dca39f1b7cedf13feb808
S_17 mod 7; pypdf 6.16.2
pages: 135, sections: 144; row blocks: 8; column blocks: 18
title line: 'A17.2 (mod 7)'
partitions of 17: 297; rows found: 297; columns: 252; distinct label strings among the partitions: 296
parse problems: 0
r-regular partitions: 252; columns = r-regular partitions with unitriangular block (James): True
r-regular classes: 252 (must equal the number of columns: True)
M B = X on all 297 rows x 252 classes: inconsistent pairs = 0; degrees positive: True
block check (nonzero decomposition numbers only between partitions with the same 7-core): violations = 0; blocks: 69, of defect zero (7-cores of size 17): 45
columns with a single nonzero entry: 45; single +1 alterations invisible to M B = X (and to unitriangularity and positive degrees): 4830; all of them violate the block check
17-cycle: fixed-space dimensions integral and >= 0: True; fixed-point-free on 2 simple module(s): ϕ3 = D^(16, 1) dim 16 [N]; ϕ4 = D^(3, 3, 3, 3, 2, 2, 1) dim 16 [N(x)sgn]; max |beta(x)| = 2
  list is exactly {N, N (x) sgn}: True
negative controls: entry (17101, ϕ1) + 1 -> 252 inconsistent pairs; entry (162271, ϕ1) + 1 -> 0 inconsistent pairs
