{
  "abstract": "We classify the complementary vectors of doubly Cohen–Macaulay complexes. This proves a conjecture of Swartz, negatively answers a question of Athanasiadis and Tzanaki, and gives new bounds on the number of independent sets in a matroid. Our technique works more generally for certain level quotients of Stanley–Reisner rings, giving new bounds on the face numbers of Buchsbaum* complexes.",
  "abstract_shown": true,
  "affiliations": [
    "Princeton University",
    "Sydney Mathematics Research Institute"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Matt Larson"
    },
    {
      "affs": [
        1
      ],
      "name": "Alan Stapledon"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2gf0646h0r5g8.bib",
  "cited_by": 1,
  "doi": "10.1017/fms.2026.10288",
  "fulltext_url": null,
  "id": "2gf0646h0r5g8",
  "issns": [
    "2050-5094"
  ],
  "landing_url": "https://www.cambridge.org/core/product/identifier/S2050509426102886/type/journal_article",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W4417168565",
  "pdf_url": "https://www.cambridge.org/core/services/aop-cambridge-core/content/view/27A13C257BF97E542E21509201273176/S2050509426102886a.pdf/div-class-title-complementary-vectors-of-simplicial-complexes-div.pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": "Cambridge University Press (CUP)",
  "ris": "https://research.draconitic.com/paper/2gf0646h0r5g8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:20Z",
      "native_id": "10.1017/fms.2026.10288",
      "source": "crossref",
      "url": "https://www.cambridge.org/core/product/identifier/S2050509426102886/type/journal_article"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2607|Advanced Combinatorial Mathematics",
      "subfield": "combinatorics"
    }
  ],
  "title": "Complementary vectors of simplicial complexes",
  "title_text": "Complementary vectors of simplicial complexes",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/2gf0646h0r5g8",
  "venue": "Forum of Mathematics, Sigma",
  "versions": []
}