{
  "abstract": "Seeking to bridge the structural divide between a permutation's cycle notation and its one-line notation, Berman and Tenner introduced a novel notion of permutation pattern known as the arrow pattern. Recently, Archer and Laudone initiated a systematic study of arrow pattern avoidance, leaving behind three intriguing conjectures. In this paper, we resolve all three conjectures. First, we enumerate all six subclasses of permutations that simultaneously avoid a classical pattern of length 3 and a fixed arrow pattern of length 3, thereby confirming the first two conjectures. Second, we settle the third conjecture (which involves a different arrow pattern) by providing two independent proofs. These proofs rely on a restriction of Biane's bijection to non-nesting involutions and Krattenthaler's bijection from 321-avoiding permutations to Dyck paths, respectively.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.04094",
  "author_total": 2,
  "authors": [
    {
      "name": "Shishuo Fu"
    },
    {
      "name": "Zhenghe Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/42r2aapng804v.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.04094",
  "fulltext_url": null,
  "id": "42r2aapng804v",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.04094",
  "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",
      "cs.DM"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7167642461",
  "pdf_url": "https://arxiv.org/pdf/2607.04094",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/42r2aapng804v.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2607.04094",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.04094"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "When arrow patterns meet classical patterns",
  "title_text": "When arrow patterns meet classical patterns",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/42r2aapng804v",
  "venue": "arXiv",
  "versions": []
}