{
  "abstract": "We establish a sufficient condition for infinite log-concavity and apply it to five families of combinatorial sequences. We give a new proof of infinite log-concavity for the Boros--Moll coefficient sequences $(d_k(n))_{k=0}^n$ for fixed $n$. For the transposed sequences $(d_\\ell(\\ell+k))_{k\\ge0}$, we prove Zhao's conjecture on infinite log-concavity for every fixed integer $\\ell\\ge3$. For the normalized sequences in Euler's difference table, we confirm the infinite log-concavity conjecture of Chen, Gu, Ma and Wang under essential iteration, in which both endpoints are discarded after each step. We also confirm a conjecture of Medina, Moll and Rowland on the infinite log-concavity of the coefficient sequences of polynomials arising from iterated primitives of $\\log(1+x)$. Finally, we answer a question of Brändén and Chasse by showing that, for positive integers $d$, the sequence $(k^d)_{k\\ge0}$ is infinitely log-concave if and only if $d\\ne2$. For every real $d\\ge3$, all its iterates are positive at every index $k\\ge1$. The proofs combine holomorphic estimates with finite computer-assisted verification.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12237",
  "author_total": 3,
  "authors": [
    {
      "name": "Matthew H. Y. Xie"
    },
    {
      "name": "Candice X. T. Zhang"
    },
    {
      "name": "Philip B. Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b123exsnepk28.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12237",
  "fulltext_url": null,
  "id": "b123exsnepk28",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12237",
  "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": "W7221100655",
  "pdf_url": "https://arxiv.org/pdf/2610.12237",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b123exsnepk28.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.12237",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12237"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A unified approach to infinite log-concavity of combinatorial sequences",
  "title_text": "A unified approach to infinite log-concavity of combinatorial sequences",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/b123exsnepk28",
  "venue": "arXiv",
  "versions": []
}