{
  "id": "2408.02425",
  "version": "v1",
  "published": "2024-08-05T12:32:21.000Z",
  "updated": "2024-08-05T12:32:21.000Z",
  "title": "Gapset Extensions, Theory and Computations",
  "authors": [
    "Arman Ataei Kachouei",
    "Farhad Rahmati"
  ],
  "comment": "14 pages, 2 algorithms",
  "categories": [
    "math.CO",
    "math.AC"
  ],
  "abstract": "In this paper we extend some set theoretic concepts of numerical semigroups for arbitrary sub-semigroups of natural numbers. Then we characterized gapsets which leads to a more efficient computational approach towards numerical semigroups and finally we introduce the extension of gapsets and prove that the sequence of the number of gapsets of size $g$ is non-decreasing as a weak version of Bras-Amor\\'os's conjecture.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-05T12:32:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "gapset extensions",
      "computations",
      "set theoretic concepts",
      "numerical semigroups",
      "efficient computational approach"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}