{
  "id": "2012.00476",
  "version": "v1",
  "published": "2020-12-01T13:29:33.000Z",
  "updated": "2020-12-01T13:29:33.000Z",
  "title": "Families of finite sets in which no set is covered by the union of the others",
  "authors": [
    "Guillermo Alesandroni"
  ],
  "categories": [
    "math.CO",
    "math.AC"
  ],
  "abstract": "Let F be a finite family of finite sets. We prove the following: (i) F satisfies the condition of the title if and only if for every pair of distinct subfamilies {A_1,...,A_r}, {B_1,...,B_s} of F, the union of the A_i is different from the union of the B_i. (ii) If F satisfies the condition of the title, then the number of subsets of the union of the members of F containing at least one set of F is odd. We give two applications of these results, one to number theory and one to commutative algebra.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-01T13:29:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite sets",
      "number theory",
      "distinct subfamilies",
      "applications",
      "commutative algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}