{
  "abstract": "For a numerical semigroup $S$ with Frobenius number $F$ and gaps $G$, a polynomial $P\\left(z\\right)=\\sum_{g\\in G}c_{g}z^{g}$ of degree $F$ is called a gap polynomial. We show that for a symmetric numerical semigroup, the power sums of the critical points of a gap polynomial vanish for every power $g\\in G$. For a pseudo-symmetric numerical semigroup, the same result holds if the term $z^{F/2}$ is omitted from $P\\left( z\\right) $. We give several corollaries, including that the sum of the critical values of a gap polynomial vanishes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.03049",
  "author_total": 1,
  "authors": [
    {
      "name": "Pavel Grinfeld"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9vb9377vqj2sm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.03049",
  "fulltext_url": null,
  "id": "9vb9377vqj2sm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.03049",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AC"
    ],
    [
      "openalex",
      "2602|Commutative Algebra and Its Applications"
    ]
  ],
  "openalex": "W7208726083",
  "pdf_url": "https://arxiv.org/pdf/2609.03049",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9vb9377vqj2sm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:18Z",
      "native_id": "2609.03049",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.03049"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Power sums of critical points of gap polynomials for symmetric and pseudo-symmetric numerical semigroups",
  "title_text": "Power sums of critical points of gap polynomials for symmetric and pseudo-symmetric numerical semigroups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:18Z",
  "url": "https://research.draconitic.com/paper/9vb9377vqj2sm",
  "venue": "arXiv",
  "versions": []
}