{
  "id": "1808.08906",
  "version": "v1",
  "published": "2018-08-27T16:21:03.000Z",
  "updated": "2018-08-27T16:21:03.000Z",
  "title": "Statistics on Multisets",
  "authors": [
    "Shashikant Mulay",
    "Carl Wagner"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We offer a new proof that a certain q-analogue of multinomial coeffi- cients furnishes a q-counting of the set of permutations of an associated multiset of positive integers, according to the number of inversions in such arrangements. Our proof uses the fact that such q-multinomial coefficients enumerate certain classes of chains of subspaces of a fnite dimensional vector space over a fnite field of cardinality q. Additionally, we investigate the function that counts the number of permutations of a multiset having a fixed number of inversions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-27T16:21:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A05",
      "05A15"
    ],
    "keywords": [
      "statistics",
      "fnite dimensional vector space",
      "q-multinomial coefficients enumerate",
      "permutations",
      "fnite field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}