table A17.2partmod3.pdf  sha256 49454d228c20ba063cd87a10bfbe79914f74492fd3c8ed21672bf0987ee31105
S_17 mod 3; pypdf 6.16.2
pages: 60, sections: 64; row blocks: 8; column blocks: 8
title line: 'A17.2 (mod 3)'
partitions of 17: 297; rows found: 297; columns: 108; distinct label strings among the partitions: 296
parse problems: 0
r-regular partitions: 108; columns = r-regular partitions with unitriangular block (James): True
r-regular classes: 108 (must equal the number of columns: True)
M B = X on all 297 rows x 108 classes: inconsistent pairs = 0; degrees positive: True
block check (nonzero decomposition numbers only between partitions with the same 3-core): violations = 0; blocks: 8, of defect zero (3-cores of size 17): 2
columns with a single nonzero entry: 2; single +1 alterations invisible to M B = X (and to unitriangularity and positive degrees): 172; all of them violate the block check
17-cycle: fixed-space dimensions integral and >= 0: True; fixed-point-free on 2 simple module(s): ϕ4 = D^(16, 1) dim 16 [N]; ϕ3 = D^(8, 8, 1) dim 16 [N(x)sgn]; max |beta(x)| = 2
  list is exactly {N, N (x) sgn}: True
negative controls: entry (13141, ϕ1) + 1 -> 108 inconsistent pairs; entry (21314181, ϕ4) + 1 -> 3026 inconsistent pairs
