{
  "id": "0709.2930",
  "version": "v1",
  "published": "2007-09-18T22:30:48.000Z",
  "updated": "2007-09-18T22:30:48.000Z",
  "title": "Asymptotic estimates for phi functions for subsets of {m+1, m+2,...,n}",
  "authors": [
    "Melvyn B. Nathanson",
    "Brooke Orosz"
  ],
  "comment": "5 pages",
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "Let f(m,n) denote the number of relatively prime subsets of {m+1,m+2,...,n}, and let Phi(m,n) denote the number of subsets A of {m+1,m+2,...,n} such that gcd(A) is relatively prime to n. Let f_k(m,n) and Phi_k(m,n) be the analogous counting functions restricted to sets of cardinality k. Simple explicit formulas and asymptotic estimates are obtained for these four functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-09-18T22:30:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A25",
      "11B05",
      "11B13",
      "11B75"
    ],
    "keywords": [
      "asymptotic estimates",
      "phi functions",
      "simple explicit formulas",
      "relatively prime subsets",
      "cardinality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0709.2930N"
    }
  }
}