bibkey: shankar2026canon authors: Umesh Shankar year: 2026 title: Avoiding patterns with three distinct letters in Canon permutations doi: 10.48550/arXiv.2608.30002 claim: Theorem 7.1 identifies Q with the stated ballot-binomial closed form; Conjecture 9.5 asserts that B and Q are Stieltjes moment sequences. strata_touched:

• D5/S0/Certificates/ShankarQStieltjesRefutation license: citation-only triage: anchor

Avoiding patterns with three distinct letters in Canon permutations

Version 2, sections 2.2, 2.7, 7, and 9 were read. Q counts the lattice words with k occurrences each of 1, 2, and 3 that avoid the subsequence 321. Theorem 7.1 gives the formula transcribed by closedFormQ, with Q(0)=1 and zero binomial coefficients for negative lower indices.

This note attests the source formula and conjecture, not the repository’s negative certificate or refutation. The complete combinatorial bijection behind Theorem 7.1 is a published source input, not formalized here. The repository result concerns Q only; B remains unresolved.

Verified locator

• DOI: https://doi.org/10.48550/arXiv.2608.30002
• Original version read: https://arxiv.org/html/2608.30002v2
• Formula: Theorem 7.1, equations defining E and H immediately before it.
• Target: Conjecture 9.5, both B and Q Stieltjes claims.

Bounded searches on 2026-09-06 found no settlement in the checked arXiv title/identifier queries, exact-identifier GitHub results, or OpenAlex record W7204872451 (zero citing works). This supports suspected-open status only; it is not a globally certified novelty claim.