{
  "id": "0806.3046",
  "version": "v2",
  "published": "2008-06-18T16:50:12.000Z",
  "updated": "2008-09-12T16:50:16.000Z",
  "title": "A Filtration of (q,t)-Catalan numbers",
  "authors": [
    "N. Bergeron",
    "F. Descouens",
    "M. Zabrocki"
  ],
  "journal": "Adv. in Appl. Math. 44 (2010), no. 1, 16--36.",
  "categories": [
    "math.CO"
  ],
  "abstract": "We define new generalizations of (q,t)-Catalan numbers applying nabla operator on k-Schur functions indexed by column partitions. In some special cases, we give a combinatorial interpretation of these numbers using configurations of Dyck paths. In some other special cases, we also interpret these new polynomial as Hilbert series of explicit sub-modules of the alternating diagonal harmonics built using differential operators.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-09-12T16:50:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "filtration",
      "special cases",
      "numbers applying nabla operator",
      "alternating diagonal harmonics built",
      "differential operators"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0806.3046B"
    }
  }
}