{
  "abstract": "Chromatic quasisymmetric functions and unicellular LLT polynomials give symmetric-function interpretations of graph orientations counted by sinks. For natural unit interval graphs, we prove that the acyclic sink polynomial is real-rooted for every nonnegative ascent weight. Equivalently, the elementary coefficients of the chromatic quasisymmetric function, grouped by partition length, form a real-rooted polynomial. The Carlsson--Mellit relation expresses this polynomial as a plethystic specialization of the corresponding LLT polynomial, and the Hessenberg correspondence gives an interpretation in cohomology. More generally, the acyclic sink polynomial is real-rooted for chordal claw-free graphs, and the all-orientations sink polynomial is real-rooted for every claw-free graph. We also study a real-rooted polynomial counting joint minima in local edge orders. It agrees with the acyclic sink polynomial of the line graph exactly for forests. An exact formula for unicyclic roots gives a line-graph counterexample to acyclic sink real-rootedness.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.41502",
  "author_total": 2,
  "authors": [
    {
      "name": "Per Alexandersson"
    },
    {
      "name": "Leonardo Saud Maia Leite"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1jkatz9xv3grg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.41502",
  "fulltext_url": null,
  "id": "1jkatz9xv3grg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.41502",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.41502",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1jkatz9xv3grg.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2610.41502",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.41502"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Sink polynomials of line graphs and weighted matching polynomials",
  "title_text": "Sink polynomials of line graphs and weighted matching polynomials",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:52Z",
  "url": "https://research.draconitic.com/paper/1jkatz9xv3grg",
  "venue": "arXiv",
  "versions": []
}