{
  "abstract": "We give a counting formula in terms of modified Hall–Littlewood polynomials and the chromatic quasisymmetric function for the number of points on an arbitrary Hessenberg variety over a finite field. As a consequence, we express the Poincaré polynomials of complex Hessenberg varieties in terms of a Hall scalar product involving the symmetric functions above. We use these results to give a new proof of a combinatorial formula for the modified Hall–Littlewood polynomials.",
  "abstract_shown": true,
  "affiliations": [
    "Instituto de Matemática e Estatística, Universidade Federal Fluminense, Niterói, Rio de Janeiro (Brazil)",
    "Indraprastha Institute of Information Technology Delhi, New Delhi (India)"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Alex Abreu"
    },
    {
      "affs": [
        0
      ],
      "name": "Antonio Nigro"
    },
    {
      "affs": [
        1
      ],
      "name": "Samrith Ram"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/48zwmf9vnfax8.bib",
  "cited_by": 0,
  "doi": "10.5802/alco.519",
  "fulltext_url": null,
  "id": "48zwmf9vnfax8",
  "issns": [
    "2589-5486"
  ],
  "landing_url": "https://alco.centre-mersenne.org/articles/10.5802/alco.519/",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W4404389223",
  "pdf_url": "https://alco.centre-mersenne.org/item/10.5802/alco.519.pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": "MathDoc/Centre Mersenne",
  "ris": "https://research.draconitic.com/paper/48zwmf9vnfax8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:25Z",
      "native_id": "10.5802/alco.519",
      "source": "crossref",
      "url": "https://alco.centre-mersenne.org/articles/10.5802/alco.519/"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2607|Advanced Combinatorial Mathematics",
      "subfield": "combinatorics"
    }
  ],
  "title": "Counting points on Hessenberg varieties over finite fields",
  "title_text": "Counting points on Hessenberg varieties over finite fields",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:25Z",
  "url": "https://research.draconitic.com/paper/48zwmf9vnfax8",
  "venue": "Algebraic Combinatorics",
  "versions": []
}