{
  "abstract": "Stanley's conjecture asserts that the $h$-vector of a matroid is a pure $O$-sequence. Corry, Dochtermann, McClain, Perkinson and Yi introduced cycle systems, which give a bijective proof for the matroids that admit one, through coparking functions, and proposed generalized cycle systems. Every matroid admitting a cycle system is regular, and the Wagner and Petersen graphs admit no generalized cycle system consisting of circuits. We propose a relaxation. Where the coparking recursion breaks down, at the strata whose unique union is independent, the coparking functions are replaced by a fibre: a pure multicomplex with the $h$-vector of the dead node, the minor of the matroid attached to the stratum. We prove, for any matroid with a fixed basis, that whenever the required fibres exist the relaxed coparking functions form a pure multicomplex whose degree sequence is the $h$-vector of the matroid, so Stanley's conjecture follows. The proof rests on a version of Dhar's burning algorithm for a matroid with a fixed basis, which gives the purity, and on a deletion-contraction identity that computes the gap between the $h$-vector and the coparking functions as a sum of local $h$-vectors, one per dead node. Coned, biconed and triconed graphs carry a fibre system with their canonical spanning trees, as do the Wagner and Petersen graphs. Beyond graphs, every basis of a matroid of corank two, of a matroid of rank at most four or of a uniform matroid carries a fibre system, so Stanley's conjecture follows for those classes. We also give a graph of radius two on twelve vertices which, with its breadth-first spanning tree, carries no fibre system.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.17446",
  "author_total": 1,
  "authors": [
    {
      "name": "SuHo Oh"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a0fyhy50c9hzh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.17446",
  "fulltext_url": null,
  "id": "a0fyhy50c9hzh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.17446",
  "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",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7213473597",
  "pdf_url": "https://arxiv.org/pdf/2609.17446",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a0fyhy50c9hzh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.17446",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.17446"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Relaxed coparking functions and Stanley's conjecture for matroid $h$-vectors",
  "title_text": "Relaxed coparking functions and Stanley's conjecture for matroid h-vectors",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/a0fyhy50c9hzh",
  "venue": "arXiv",
  "versions": []
}