{
  "abstract": "For a permutation pi in Sk, a pi-wave is an increasing sequence of integers whose consecutive gaps have relative order pi. Let g(pi, n) be the maximum cardinality of a pi-wave-free subset of [n], and let P(pi, r) be the least integer N such that every r-coloring of [N] contains a monochromatic pi-wave. We determine the asymptotic orders of both functions for every permutation of length at most five. Existing upper bounds and weak-wave constructions provide sharp bounds for all but eight length-five patterns in S_5. For these eight exceptional alternating patterns, we establish g(pi, n) = Theta((log n)squared) and P(pi, r) = Theta(r(log r)squared).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.04184",
  "author_total": 3,
  "authors": [
    {
      "name": "Lihong Qiu"
    },
    {
      "name": "Minglei Mao"
    },
    {
      "name": "Yaping Mao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a986kvcj52aas.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.04184",
  "fulltext_url": null,
  "id": "a986kvcj52aas",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.04184",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.04184",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a986kvcj52aas.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:29Z",
      "native_id": "2611.04184",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.04184"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Short permutation pattern waves: The complete length-five classification",
  "title_text": "Short permutation pattern waves: The complete length-five classification",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/a986kvcj52aas",
  "venue": "arXiv",
  "versions": []
}