{
  "id": "0804.3074",
  "version": "v2",
  "published": "2008-04-18T17:50:56.000Z",
  "updated": "2009-06-16T19:55:49.000Z",
  "title": "(q,t)-analogues and GL_n(F_q)",
  "authors": [
    "Victor Reiner",
    "Dennis Stanton"
  ],
  "comment": "Final version to appear in J. Algebraic Combin",
  "categories": [
    "math.CO",
    "math.RT"
  ],
  "abstract": "We start with a (q,t)-generalization of a binomial coefficient. It can be viewed as a polynomial in t that depends upon an integer q, with combinatorial interpretations when q is a positive integer, and algebraic interpretations when q is the order of a finite field. These (q,t)-binomial coefficients and their interpretations generalize further in two directions, one relating to column-strict tableaux and Macdonald's ``seventh variation'' of Schur functions, the other relating to permutation statistics and Hilbert series from the invariant theory of GL_n(F_q).",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-06-16T19:55:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A17"
    ],
    "keywords": [
      "finite field",
      "combinatorial interpretations",
      "invariant theory",
      "algebraic interpretations",
      "binomial coefficient"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0804.3074R"
    }
  }
}