{
  "abstract": "After the substitution $q\\mapsto q+1$, vertical-strip LLT polynomials are weighted sums of strict $P$-partition generating functions indexed by orientations of decorated unit-interval graphs, with weight $q^{\\mathrm{asc}(θ)}$. A flip moves an ascending edge across a triangle while keeping its long edge. We show that the sum over every flip class is elementary-positive: it equals the sum of the elementary symmetric functions given by the highest reachable vertices of its orientations. This answers Hwang's question on the Schur positivity of LLT flip-class sums, and it holds for circular unit-interval graphs as well. Summing over classes gives a new proof of the elementary expansion of Alexandersson and Sulzgruber, and its circular analog, which was open. We also obtain a flip-class refinement of the elementary expansion of LLT cumulants.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.26294",
  "author_total": 2,
  "authors": [
    {
      "name": "Per Alexandersson"
    },
    {
      "name": "Lilan Dai"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c4pn0hd3vp7rx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.26294",
  "fulltext_url": null,
  "id": "c4pn0hd3vp7rx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.26294",
  "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"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7223021246",
  "pdf_url": "https://arxiv.org/pdf/2610.26294",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c4pn0hd3vp7rx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.26294",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.26294"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Flip classes and elementary expansions of vertical-strip LLT polynomials",
  "title_text": "Flip classes and elementary expansions of vertical-strip LLT polynomials",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/c4pn0hd3vp7rx",
  "venue": "arXiv",
  "versions": []
}