{
  "abstract": "We introduce a notion of a strong $\\mathfrak{sl}_2$-action on a poset, and conjecture the existence of such an action is equivalent to the existence of a symmetric chain decomposition of that poset. We explain the intuition behind the conjecture, go through a number of explicit examples, and prove some special cases and relaxations of the conjecture. Then we explain a computational experiment where we tested the conjecture on millions of randomly constructed rank-symmetric, rank-unimodal, and strongly Sperner posets.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24148",
  "author_total": 4,
  "authors": [
    {
      "name": "Nate Harman"
    },
    {
      "name": "Rylan Rosas"
    },
    {
      "name": "Charles Troutman III"
    },
    {
      "name": "Chris Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9y51hmvb39ttf.bib",
  "cited_by": 1,
  "doi": "10.48550/arxiv.2610.24148",
  "fulltext_url": null,
  "id": "9y51hmvb39ttf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24148",
  "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"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7223060181",
  "pdf_url": "https://arxiv.org/pdf/2610.24148",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9y51hmvb39ttf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.24148",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24148"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Strong $\\mathfrak{sl}_2$ Actions and Symmetric Chain Decompositions",
  "title_text": "Strong sl_2 Actions and Symmetric Chain Decompositions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/9y51hmvb39ttf",
  "venue": "arXiv",
  "versions": []
}