{
  "id": "2101.01760",
  "version": "v1",
  "published": "2021-01-05T19:53:37.000Z",
  "updated": "2021-01-05T19:53:37.000Z",
  "title": "On evenly distributed sets of gaps of numerical semigroups",
  "authors": [
    "Caleb McKinley Shor"
  ],
  "comment": "15 pages. To be submitted",
  "categories": [
    "math.NT",
    "math.GR"
  ],
  "abstract": "For a positive integer $m$, a finite set of integers is said to be evenly distributed modulo $m$ if the set contains an equal number of elements in each congruence class modulo $m$. In this paper, we consider the problem of determining when the set of gaps of a numerical semigroup $S$ is evenly distributed modulo $m$. Of particular interest is the case when the nonzero elements of an Ap\\'ery set of $S$ form an arithmetic sequence, which occurs precisely when $S$ is a numerical semigroup of embedding dimension 2 or a numerical semigroup of maximal embedding dimension generated by a generalized arithmetic sequence. We derive explicit conditions for which the gaps of these numerical semigroups are evenly distributed modulo $m$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-05T19:53:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11D04",
      "20M14"
    ],
    "keywords": [
      "numerical semigroup",
      "evenly distributed sets",
      "evenly distributed modulo",
      "arithmetic sequence",
      "embedding dimension"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}