{
  "id": "0809.4621",
  "version": "v2",
  "published": "2008-09-26T13:11:56.000Z",
  "updated": "2008-11-22T14:59:14.000Z",
  "title": "Explicit constructions of infinite families of MSTD sets",
  "authors": [
    "Steven J. Miller",
    "Brooke Orosz",
    "Daniel Scheinerman"
  ],
  "comment": "Version 2: 14 pages, 1 figure. Includes extensions to ternary forms and a conjecture for general combinations of the form Sum_i epsilon_i A with epsilon_i in {-1,1} (would be a theorem if we could find a set to start the induction in general)",
  "journal": "Journal of Number Theory 130 (2010) 1221--1233",
  "doi": "10.1016/j.jnt.2009.09.003",
  "categories": [
    "math.NT"
  ],
  "abstract": "We explicitly construct infinite families of MSTD (more sums than differences) sets. There are enough of these sets to prove that there exists a constant C such that at least C / r^4 of the 2^r subsets of {1,...,r} are MSTD sets; thus our family is significantly denser than previous constructions (whose densities are at most f(r)/2^{r/2} for some polynomial f(r)). We conclude by generalizing our method to compare linear forms epsilon_1 A + ... + epsilon_n A with epsilon_i in {-1,1}.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-11-22T14:59:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11P99",
      "11K99"
    ],
    "keywords": [
      "mstd sets",
      "explicit constructions",
      "compare linear forms",
      "explicitly construct infinite families",
      "significantly denser"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0809.4621M"
    }
  }
}