{
  "id": "2203.10376",
  "version": "v1",
  "published": "2022-03-19T18:48:39.000Z",
  "updated": "2022-03-19T18:48:39.000Z",
  "title": "On sets related to integer partitions with quasi-required elements and disallowed elements",
  "authors": [
    "Aureliano M. Robles-Pérez",
    "José Carlos Rosales"
  ],
  "comment": "17 pages",
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "Given a set A of non-negative integers and a set B of positive integers,we are interested in computing all sets C (of positive integers) that are minimal in the family of sets K (of positive integers) such that (i) K contains no elements generated by integer linear combinations of elements in A and (ii) for any partition of an element in B there is at least one summand that belongs to K. To solve this question, we translate it into a numerical semigroups problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-19T18:48:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A17",
      "11P81",
      "20M14"
    ],
    "keywords": [
      "integer partitions",
      "quasi-required elements",
      "disallowed elements",
      "positive integers",
      "integer linear combinations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}