{
  "id": "2304.13690",
  "version": "v1",
  "published": "2023-04-26T17:16:35.000Z",
  "updated": "2023-04-26T17:16:35.000Z",
  "title": "Counting Ideals in Numerical Semigroups",
  "authors": [
    "Parth Chavan"
  ],
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "We calculate the ideal generating function counting ideals in a numerical semigroup with respect to their codimension for numerical semigroups with embedding dimension $2$ and certain families of numerical semigroups with embedding dimension $3.$ We also show that the degree of the ideal generating function of a numerical semigroup is its Frobenius number.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-26T17:16:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20M14",
      "05A19"
    ],
    "keywords": [
      "numerical semigroup",
      "ideal generating function counting ideals",
      "embedding dimension",
      "frobenius number",
      "codimension"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}