{
  "abstract": "Let ${S}_n(321)$ and ${S}_n(\\underline{321})$ denote the sets of $n$-permutations avoiding the classical pattern $321$ and the consecutive pattern $\\underline{321}$, respectively. Permutations are in bijection with Lehmer codes, a type of inversion sequence. Using Lehmer codes, we create the corresponding weighted posets ${L}_n(321)$ and ${L}_n(\\underline{321})$, where the weight of a code is the inversion number of its permutation. We show that there are $2^{n-2}$ maximal elements of ${L}_n(321)$, while the maximal elements of ${L}_n(\\underline{321})$ are enumerated by the Padovan numbers. We also show that when $n$ is even, each of these posets has a unique maximum weight element, and that when $n$ is odd, there are two maximum weight elements. These maximum weight Lehmer codes correspond to the pattern avoiding permutations with maximum inversion number.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.33137",
  "author_total": 3,
  "authors": [
    {
      "name": "Andrew Beveridge"
    },
    {
      "name": "Yufan Hu"
    },
    {
      "name": "Yucheng Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/21ze6hpsr994t.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.33137",
  "fulltext_url": null,
  "id": "21ze6hpsr994t",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.33137",
  "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": "W7214801907",
  "pdf_url": "https://arxiv.org/pdf/2609.33137",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/21ze6hpsr994t.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.33137",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.33137"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Maximal Lehmer Codes for Permutations with Classical and Consecutive 321-Avoidance",
  "title_text": "Maximal Lehmer Codes for Permutations with Classical and Consecutive 321-Avoidance",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/21ze6hpsr994t",
  "venue": "arXiv",
  "versions": []
}