{
  "id": "2001.00280",
  "version": "v1",
  "published": "2020-01-01T23:36:21.000Z",
  "updated": "2020-01-01T23:36:21.000Z",
  "title": "Permutations, moments, measures",
  "authors": [
    "Natasha Blitvić",
    "Einar Steingrímsson"
  ],
  "comment": "This is an extended abstract, submitted on November 20, 2019 to the conference Formal Power Series and Algebraic Combinatorics, of a longer paper to appear soon on arXiv",
  "categories": [
    "math.CO",
    "math.PR"
  ],
  "abstract": "We present a continued fraction with 13 permutation statistics, several of them new, connecting a great number of combinatorial structures to a wide variety of moment sequences and their measures from classical and noncommutative probability. The Hankel determinants of these moment sequences are a product of $(p,q)$-factorials, unifying several instances from the literature. The corresponding measures capture as special cases several classical laws, such as the Gaussian, Poisson, and exponential, along with further specializations of the orthogonalizing measures in the Askey-Wilson scheme and several known noncommutative central limits. Statistics in our continued fraction generalize naturally to signed and colored permutations, and to the $k$-arrangements introduced here, permutations with $k$-colored fixed points.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-01T23:36:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "moment sequences",
      "continued fraction",
      "hankel determinants",
      "combinatorial structures",
      "wide variety"
    ],
    "tags": [
      "conference paper"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}