{
  "abstract": "We give a complete classification of Schur positivity for three-legged spiders. Every spider with at least two even legs is Schur positive, whereas every spider with three odd legs has a negative Schur coefficient. If $a$ is even and $b,c$ are odd, then the spider $S(a,b,c)$ is Schur positive if and only if $a\\le 5b+5c+2$. Whenever Schur positivity fails, there is exactly one negative Schur coefficient, whose value we determine explicitly. These results extend those of Thibon and Wang for the families $S(a,2,1)$ and $S(a,4,1)$, and those of Wang and Wang for $S(a,b,2)$. The proof combines known Schur-positivity results for clique-spiders with Pieri's rule and simultaneous induction.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03464",
  "author_total": 2,
  "authors": [
    {
      "name": "David G. L. Wang"
    },
    {
      "name": "Watson Z. Y. Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0f92xjyrcre0r.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03464",
  "fulltext_url": null,
  "id": "0f92xjyrcre0r",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03464",
  "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": "W7220389854",
  "pdf_url": "https://arxiv.org/pdf/2610.03464",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0f92xjyrcre0r.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2610.03464",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03464"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Schur positivity of three-legged spiders",
  "title_text": "Schur positivity of three-legged spiders",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/0f92xjyrcre0r",
  "venue": "arXiv",
  "versions": []
}