{
  "abstract": "We establish formulas for the Hilbert series of the Chow ring of a polymatroid using arbitrary building sets. For braid matroids and minimal building sets, our results produce new formulas for the Poincaré polynomial of the moduli space $$\\overline{\\mathcal {M}}_{0,n+1}$$ M ¯ 0 , n + 1 of pointed stable rational curves, and recover several previous results by Keel, Getzler, Manin, and Aluffi–Marcolli–Nascimento. We also use our methods to produce examples of matroids and building sets for which the corresponding Chow ring has Hilbert series with non-log-concave coefficients. This contrasts with the real-rootedness and log-concavity conjectures of Ferroni–Schröter for matroids with maximal building sets, and of Aluffi–Chen–Marcolli for braid matroids with minimal building sets.",
  "abstract_shown": true,
  "affiliations": [
    "Carnegie Mellon University, Pittsburgh, PA, USA",
    "Università di Pisa, Pisa, Italy",
    "North Carolina State University, Raleigh, NC, USA",
    "Università di Bologna, Bologna, Italy",
    "KTH Royal Institute of Technology, Stockholm, Sweden"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 5,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Christopher Eur",
      "orcid": "0000-0002-0324-1139"
    },
    {
      "affs": [
        1
      ],
      "name": "Luis Ferroni",
      "orcid": "0000-0001-5181-7932"
    },
    {
      "affs": [
        2
      ],
      "name": "Jacob P. Matherne",
      "orcid": "0000-0002-6187-9771"
    },
    {
      "affs": [
        3
      ],
      "name": "Roberto Pagaria",
      "orcid": "0000-0002-2231-4006"
    },
    {
      "affs": [
        4
      ],
      "name": "Lorenzo Vecchi",
      "orcid": "0000-0002-5923-0471"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/09t640gprky5h.bib",
  "cited_by": 13,
  "doi": "10.1007/s00029-026-01186-2",
  "fulltext_url": null,
  "id": "09t640gprky5h",
  "issns": [
    "1022-1824",
    "1420-9020"
  ],
  "landing_url": "https://doi.org/10.1007/s00029-026-01186-2",
  "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": "W4415066958",
  "pdf_url": "https://link.springer.com/content/pdf/10.1007/s00029-026-01186-2.pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-11",
  "publisher": "Birkhäuser",
  "ris": "https://research.draconitic.com/paper/09t640gprky5h.ris",
  "sources": [
    {
      "first_seen": "2026-11-07T13:20:42Z",
      "native_id": "W4415066958",
      "source": "openalex",
      "url": "https://doi.org/10.1007/s00029-026-01186-2"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2607|Advanced Combinatorial Mathematics",
      "subfield": "combinatorics"
    }
  ],
  "title": "Building sets, Chow rings, and their Hilbert series",
  "title_text": "Building sets, Chow rings, and their Hilbert series",
  "type": "peer-reviewed",
  "updated_at": "2026-11-09T13:21:00Z",
  "url": "https://research.draconitic.com/paper/09t640gprky5h",
  "venue": "Selecta Mathematica",
  "versions": []
}