{
  "id": "1109.3353",
  "version": "v3",
  "published": "2011-09-15T14:06:17.000Z",
  "updated": "2013-05-21T13:24:52.000Z",
  "title": "Euler-Mahonian Statistics via Polyhedral Geometry",
  "authors": [
    "Matthias Beck",
    "Benjamin Braun"
  ],
  "comment": "version 3 contains a corrected version of one of the type B theorems and omits a type D result",
  "journal": "Advances in Mathematics 244 (2013), 925-954",
  "categories": [
    "math.CO"
  ],
  "abstract": "A variety of descent and major-index statistics have been defined for symmetric groups, hyperoctahedral groups, and their generalizations. Typically associated to pairs of such statistics is an Euler--Mahonian distribution, a bivariate generating function identity encoding these statistics. We use techniques from polyhedral geometry to establish new multivariate generalizations for many of the known Euler--Mahonian distributions. The original bivariate distributions are then straightforward specializations of these multivariate identities. A consequence of these new techniques are bijective proofs of the equivalence of the bivariate distributions for various pairs of statistics.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-05-21T13:24:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "polyhedral geometry",
      "euler-mahonian statistics",
      "generating function identity encoding",
      "euler-mahonian distribution",
      "bivariate generating function identity"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier",
      "journal": "Adv. Math."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1109.3353B"
    }
  }
}