{
  "id": "0909.0086",
  "version": "v2",
  "published": "2009-09-01T04:44:10.000Z",
  "updated": "2010-02-16T03:45:31.000Z",
  "title": "$(q,t)$-deformations of multivariate hook product formulae",
  "authors": [
    "Soichi Okada"
  ],
  "comment": "Improvement of Proposition 4.5 and minor revision",
  "categories": [
    "math.CO"
  ],
  "abstract": "We generalize multivariate hook product formulae for $P$-partitions. We use Macdonald symmetric functions to prove a $(q,t)$-deformation of Gansner's hook product formula for the generating functions of reverse (shifted) plane partitions. (The unshifted case has also been proved by Adachi.) For a $d$-complete poset, we present a conjectural $(q,t)$-deformation of Peterson--Proctor's hook product formula.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-02-16T03:45:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E05"
    ],
    "keywords": [
      "deformation",
      "gansners hook product formula",
      "peterson-proctors hook product formula",
      "generalize multivariate hook product formulae",
      "macdonald symmetric functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0909.0086O"
    }
  }
}