{
  "id": "1502.05340",
  "version": "v1",
  "published": "2015-02-18T18:57:26.000Z",
  "updated": "2015-02-18T18:57:26.000Z",
  "title": "Sieved Enumeration of Interval Orders and Other Fishburn Structures",
  "authors": [
    "Stuart A. Hannah"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Following a result of Eriksen and Sj\\\"{o}strand we detail a technique to construct structures following the Fishburn distribution from appropriate Mahonian structures. This technique is introduced on a bivincular pattern of Bousquet-M\\'elou et al. (2010) and then used to introduce a previously unconsidered class of matchings; explicitly, zero alignment matchings according to the number of arcs which are both right-crossed and left nesting. We then define a statistic on the factorial posets of Claesson and Linusson (2011) which we refer to as mislabelings and demonstrate that according to mislabelings factorial posets follow the Fishburn distribution. As a consequence of our approach we find an identity for the Fishburn numbers in terms of the Mahonian numbers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-02-18T18:57:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A15"
    ],
    "keywords": [
      "interval orders",
      "fishburn structures",
      "sieved enumeration",
      "fishburn distribution",
      "appropriate mahonian structures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}