bibkey: kallat2026weightedpermutations
authors: Ahaan Kallat
year: 2026
title: "Universal Shift Congruences for Weighted Permutation Sequences"
doi: 10.48550/arXiv.2610.15849
url: https://arxiv.org/abs/2610.15849v1
claim: "Section 9.2 and the supplementary open-problem catalogue place the stronger A378495 column identities beyond the permutation congruences established in v1."
strata_touched:
  - D5/S3/Combinatorics/Derangements/TerminalDifference
  - D5/S3/Combinatorics/Derangements/AdjacentDifferenceRefutation
license: citation-only
triage: anchor

Weighted permutation congruences and the two column identities

The version read is arXiv:2610.15849v1, submitted 11 October 2026. The bounded reading covers main section 9.2 and the supplementary supplementary_catalogue.tex, section sec:open, especially the A378495 discussion at source lines 478-481. It places the stronger A378495 column identities beyond the results established there. The supplementary section begins at line 469; line numbers here locate that exact version.

This source is literature context, not a Lean dependency or a proof of either original identity. The repository’s terminal identity follows from actual cycle-type cardinalities. The separate adjacent identity with literal zero-based index $n-4$ fails at $n=5$.

The bounded qualification at repository pin 0a10157da355f1825f38212dd4c2869925ae6785 read this passage and the OEIS sources. The arXiv identifier occurs in unrelated dossiers, so a broad whole-paper nonhit is not asserted. OpenAlex and Semantic Scholar search HTTP 429 gaps remain; no global novelty, priority or complete-literature claim follows from this reading. No conclusion about failure of the paper’s other theorems follows from the adjacent counterexample.