{
  "id": "0707.2707",
  "version": "v1",
  "published": "2007-07-18T12:05:36.000Z",
  "updated": "2007-07-18T12:05:36.000Z",
  "title": "A superadditivity and submultiplicativity property for cardinalities of sumsets",
  "authors": [
    "Katalin Gyarmati",
    "Imre Z. Ruzsa",
    "Mate Matolcsi"
  ],
  "comment": "9 pages",
  "categories": [
    "math.CO",
    "math.AC"
  ],
  "abstract": "For finite sets of integers $A_1, A_2 ... A_n$ we study the cardinality of the $n$-fold sumset $A_1+... +A_n$ compared to those of $n-1$-fold sumsets $A_1+... +A_{i-1}+A_{i+1}+... A_n$. We prove a superadditivity and a submultiplicativity property for these quantities. We also examine the case when the addition of elements is restricted to an addition graph between the sets.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-07-18T12:05:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B50",
      "11B75",
      "11P70"
    ],
    "keywords": [
      "submultiplicativity property",
      "cardinality",
      "superadditivity",
      "fold sumset"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0707.2707G"
    }
  }
}