{
  "id": "1010.5288",
  "version": "v1",
  "published": "2010-10-26T00:04:10.000Z",
  "updated": "2010-10-26T00:04:10.000Z",
  "title": "Generator Sets for the Alternating Group",
  "authors": [
    "Aviv Rotbart"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Although the alternating group is an index 2 subgroup of the symmetric group, there is no generating set that gives a Coxeter structure on it. Various generating sets were suggested and studied by Bourbaki, Mitsuhashi, Regev-Roichman, Vershik-Vserminov and others. In a recent work of Brenti- Reiner-Roichman it is explained that palindromes in Mitsuhashi's generating set play a role similar to that of re ections in a Coxeter system. We study in detail the length function with respect to the set of palindromes. Results include an explicit combinatorial description, a generating function, and an interesting connection to Broder's restricted Stirling numbers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-10-26T00:04:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "alternating group",
      "generator sets",
      "mitsuhashis generating set play",
      "explicit combinatorial description",
      "coxeter structure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1010.5288R"
    }
  }
}