{
  "abstract": "We define an invariant of alternating links---a homogeneous, four-variable Laurent polynomial---that encodes the symmetrized Alexander polynomial, the signature, and other topological data. Along the way, we extend a spanning tree formulation of the Alexander polynomial due to Murasugi and Stoimenow from special alternating links to all alternating links. This project is motivated by Fox's trapezoidal conjecture; accordingly, we prove certain sequences associated to our invariant are trapezoidal for all alternating links. We also conjecture our polynomial has $M$-convex support, and that it satisfies symmetry and log-concavity properties. We prove a partial symmetry result.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.28484",
  "author_total": 1,
  "authors": [
    {
      "name": "Joe Boninger"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/91yj687tkdmc8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.28484",
  "fulltext_url": null,
  "id": "91yj687tkdmc8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.28484",
  "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.GT"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7204838544",
  "pdf_url": "https://arxiv.org/pdf/2608.28484",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/91yj687tkdmc8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:28Z",
      "native_id": "2608.28484",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.28484"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "An Alexander Polynomial Refinement for Alternating Links, with Trapezoidal Properties",
  "title_text": "An Alexander Polynomial Refinement for Alternating Links, with Trapezoidal Properties",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:28Z",
  "url": "https://research.draconitic.com/paper/91yj687tkdmc8",
  "venue": "arXiv",
  "versions": []
}