{
  "abstract": "Using a dioid algebraic structure, we show that there exist spherically symmetric trees $T(2^m 1^n)$ whose independence polynomials exhibit multiple breaks in log-concavity, a result established by estimating the asymptotic growth of the coefficients of these polynomials. Provided the parameter $n$ is a sufficiently large odd integer, the number of breaks is bounded below by the Jacobsthal numbers. This result affirmatively answers a question raised by F. Bencs [D. Galvin, Trees with non log-concave independent set sequences, arXiv 2502.10654.v2].",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.04172",
  "author_total": 1,
  "authors": [
    {
      "name": "César Bautista-Ramos"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1nmmvwe0arqk9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.04172",
  "fulltext_url": null,
  "id": "1nmmvwe0arqk9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.04172",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7220691418",
  "pdf_url": "https://arxiv.org/pdf/2610.04172",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1nmmvwe0arqk9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.04172",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.04172"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Unbounded log-concavity breaks in independence polynomials of spherically symmetric trees",
  "title_text": "Unbounded log-concavity breaks in independence polynomials of spherically symmetric trees",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/1nmmvwe0arqk9",
  "venue": "arXiv",
  "versions": []
}