{
  "id": "1307.6316",
  "version": "v1",
  "published": "2013-07-24T07:56:04.000Z",
  "updated": "2013-07-24T07:56:04.000Z",
  "title": "On sumsets and convex hull",
  "authors": [
    "Karoly Boroczky",
    "Francisco Santos",
    "Oriol Serra"
  ],
  "categories": [
    "math.CO",
    "math.NT"
  ],
  "abstract": "One classical result of Freimann gives the optimal lower bound for the cardinality of A+A if A is a d-dimensional finite set in the Euclidean d-space. Matolcsi and Ruzsa have recently generalized this lower bound to |A+kB| if B is d-dimensional, and A is contained in the convex hull of B. We characterize the equality case of the Matolcsi-Ruzsa bound. The argument is based partially on understanding triangulations of polytopes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-07-24T07:56:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "convex hull",
      "optimal lower bound",
      "d-dimensional finite set",
      "matolcsi-ruzsa bound",
      "euclidean d-space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1307.6316B"
    }
  }
}