{
  "id": "1107.5070",
  "version": "v2",
  "published": "2011-07-25T20:31:55.000Z",
  "updated": "2012-01-31T20:06:36.000Z",
  "title": "The Möbius function of generalized subword order",
  "authors": [
    "Peter R. W. McNamara",
    "Bruce E. Sagan"
  ],
  "comment": "29 pages, 4 figures. Incorporates referees' suggestions; to appear in Advances in Mathematics",
  "journal": "Advances in Mathematics, 229 (5) (2012), 2741-2766",
  "categories": [
    "math.CO",
    "math.AT"
  ],
  "abstract": "Let P be a poset and let P* be the set of all finite length words over P. Generalized subword order is the partial order on P* obtained by letting u \\leq w if and only if there is a subword u' of w having the same length as u such that each element of u is less than or equal to the corresponding element of u' in the partial order on P. Classical subword order arises when P is an antichain, while letting P be a chain gives an order on compositions. For any finite poset P, we give a simple formula for the Mobius function of P* in terms of the Mobius function of P. This permits us to rederive in a easy and uniform manner previous results of Bjorner, Sagan and Vatter, and Tomie. We are also able to determine the homotopy type of all intervals in P* for any finite P of rank at most 1.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-01-31T20:06:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "06A07",
      "05A05",
      "55P15",
      "68R15"
    ],
    "keywords": [
      "generalized subword order",
      "möbius function",
      "partial order",
      "mobius function",
      "finite length words"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier",
      "journal": "Adv. Math."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1107.5070M"
    }
  }
}