{
  "abstract": "Beke, Csáji, Csikvári, and Pituk showed that the Merino--Welsh quotient $Φ(M)=T_M(1,1)^2/(T_M(2,0)T_M(0,2))$ can be arbitrarily large, so the multiplicative Merino-Welsh inequality fails for matroids in general. We show that $Φ$ is uniformly bounded on the class of matroids whose cyclic-flat lattice avoids any fixed finite poset $P$ as an induced subposet. We further prove $Φ(M)\\leq1$ for matroids of cyclic width at most $7$, cyclic height at most $6$, and for loop- and coloop-free $4$-paving or $4$-copaving matroids.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.38047",
  "author_total": 3,
  "authors": [
    {
      "name": "Kolja Knauer"
    },
    {
      "name": "Leonardo Martínez-Sandoval"
    },
    {
      "name": "Criel Merino"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2enst61yhneag.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.38047",
  "fulltext_url": null,
  "id": "2enst61yhneag",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.38047",
  "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": "W7214923522",
  "pdf_url": "https://arxiv.org/pdf/2609.38047",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2enst61yhneag.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.38047",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.38047"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Merino-Welsh inequalities for matroids with controlled lattices of cyclic flats",
  "title_text": "Merino-Welsh inequalities for matroids with controlled lattices of cyclic flats",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/2enst61yhneag",
  "venue": "arXiv",
  "versions": []
}