{
  "abstract": "We study avoidance of patterns of length $3$ with three distinct letters in canon permutations. We reduce the problem to studying pattern avoidance in lattice words and show that there are $6$ such pattern avoiding classes. This shows that there are $12$ classes for the original Canon permutation pattern avoidance problem. We also give descent refinements for these classes and classify the patterns for which the descent enumeration gives palindromic and $γ$-positive polynomials. When the polynomials are $γ$-positive, we explain the $γ$-positivity through a group action analogous to Foata-Strehl valley hopping. Additionally, we study the avoidance of patterns in the relabelling orbit of $1213, 12112, 1231$ after a conjecture about their cardinalities by Laudone and give bijective proofs for the results.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.30002",
  "author_total": 1,
  "authors": [
    {
      "name": "Umesh Shankar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1pt9kq4qf3fnp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.30002",
  "fulltext_url": null,
  "id": "1pt9kq4qf3fnp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.30002",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7204872451",
  "pdf_url": "https://arxiv.org/pdf/2608.30002",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1pt9kq4qf3fnp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:04Z",
      "native_id": "2608.30002",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.30002"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Avoiding patterns with three distinct letters in Canon permutations",
  "title_text": "Avoiding patterns with three distinct letters in Canon permutations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:04Z",
  "url": "https://research.draconitic.com/paper/1pt9kq4qf3fnp",
  "venue": "arXiv",
  "versions": []
}