{
  "abstract": "The Stanley–Stembridge conjecture asserts that the chromatic symmetric function of the incomparability graph of a ( 3 + 1 ) (3+1) -free poset is 𝑒-positive. Recently, Hikita proved this conjecture by giving an explicit 𝑒-expansion of the Shareshian–Wachs 𝑞-chromatic refinement for unit interval graphs. Using the A q , t \\mathbb{A}_{q,t} algebra, we give an expansion of these 𝑞-chromatic symmetric functions into Macdonald polynomials. Upon setting t = 1 t=1 , we obtain another proof of the Stanley–Stembridge conjecture and re-derive Hikita’s formula. Upon setting t = 0 t=0 , we obtain an expansion into Hall–Littlewood symmetric functions.",
  "abstract_shown": true,
  "affiliations": [
    "Fakultät für Mathematik , Universität Wien , Wien , Austria . Current address: Department of Mathematics, University of North Texas, Denton, TX 76203, USA",
    "Fakultät für Mathematik , Universität Wien , Wien , Austria",
    "Department of Mathematics and Statistics , Minnesota State University, Mankato , Mankato , MN 560001 , United States"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 5,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Sean T. Griffin",
      "orcid": "0000-0001-9037-5137"
    },
    {
      "affs": [
        1
      ],
      "name": "Anton Mellit",
      "orcid": "0000-0003-1287-4728"
    },
    {
      "affs": [
        2
      ],
      "name": "Marino Romero",
      "orcid": "0000-0002-7255-3179"
    },
    {
      "affs": [
        1
      ],
      "name": "Kevin Weigl"
    },
    {
      "affs": [
        1
      ],
      "name": "Joshua Jeishing Wen",
      "orcid": "0000-0002-5800-4165"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9r6xtns04pex1.bib",
  "cited_by": 14,
  "doi": "10.1515/crelle-2026-0086",
  "fulltext_url": null,
  "id": "9r6xtns04pex1",
  "issns": [
    "0075-4102",
    "1435-5345"
  ],
  "landing_url": "https://doi.org/10.1515/crelle-2026-0086",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W4417248184",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": "De Gruyter",
  "ris": "https://research.draconitic.com/paper/9r6xtns04pex1.ris",
  "sources": [
    {
      "first_seen": "2026-11-07T13:20:41Z",
      "native_id": "W4417248184",
      "source": "openalex",
      "url": "https://doi.org/10.1515/crelle-2026-0086"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2607|Advanced Combinatorial Mathematics",
      "subfield": "combinatorics"
    }
  ],
  "title": "On Macdonald expansions of 𝑞-chromatic symmetric functions and the Stanley–Stembridge conjecture",
  "title_text": "On Macdonald expansions of 𝑞-chromatic symmetric functions and the Stanley–Stembridge conjecture",
  "type": "peer-reviewed",
  "updated_at": "2026-11-08T13:20:36Z",
  "url": "https://research.draconitic.com/paper/9r6xtns04pex1",
  "venue": "Journal für die reine und angewandte Mathematik (Crelles Journal)",
  "versions": []
}