{
  "abstract": "Let $(d_i(n))_{i=0}^n$ be the Boros--Moll coefficient sequence. We prove that, for every integer $n\\ge1$, the polynomial \\[ M_n(x)=\\sum_{i=0}^n \\bigl(d_i(n)^2-d_{i-1}(n)d_{i+1}(n)\\bigr)x^i \\] has only simple negative zeros, which strictly interlace those of the Narayana polynomial of the same degree. This proves a conjecture of Chen, Yang, and Zhang and, by Brändén's preservation theorem, settles the infinite log-concavity conjecture of Boros and Moll. The proof uses an expansion of the reversed and normalized form of $M_n(x)$ in derivatives of the Narayana polynomial, together with estimates for the weights and partial sums of the normalized derivatives.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20653",
  "author_total": 2,
  "authors": [
    {
      "name": "Matthew H. Y. Xie"
    },
    {
      "name": "Philip B. Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d7g1nnwhh2dpn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20653",
  "fulltext_url": null,
  "id": "d7g1nnwhh2dpn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20653",
  "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": "W7213605796",
  "pdf_url": "https://arxiv.org/pdf/2609.20653",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d7g1nnwhh2dpn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.20653",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20653"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Infinite log-concavity of the Boros--Moll sequences",
  "title_text": "Infinite log-concavity of the Boros--Moll sequences",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/d7g1nnwhh2dpn",
  "venue": "arXiv",
  "versions": []
}