{
  "id": "0903.2555",
  "version": "v1",
  "published": "2009-03-14T16:15:29.000Z",
  "updated": "2009-03-14T16:15:29.000Z",
  "title": "Equidistribution of (X,Y)-descents, (X,Y)-adjacent pairs, and (X,Y)-place-value pairs on permutations",
  "authors": [
    "Emeric Deutsch",
    "Sergey Kitaev",
    "Jeffrey Remmel"
  ],
  "comment": "19 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "An $(X,Y)$-descent in a permutation is a pair of adjacent elements such that the first element is from $X$, the second element is from $Y$, and the first element is greater than the second one. An $(X,Y)$-adjacency in a permutation is a pair of adjacent elements such that the first one is from $X$ and the second one is from $Y$. An $(X,Y)$-place-value pair in a permutation is an element $y$ in position $x$, such that $y$ is in $Y$ and $x$ is in $X$. It turns out, that for certain choices of $X$ and $Y$ some of the three statistics above become equidistributed. Moreover, it is easy to derive the distribution formula for $(X,Y)$-place-value pairs thus providing distribution for other statistics under consideration too. This generalizes some results in the literature. As a result of our considerations, we get combinatorial proofs of several remarkable identities. We also conjecture existence of a bijection between two objects in question preserving a certain statistic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-03-14T16:15:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A15"
    ],
    "keywords": [
      "permutation",
      "equidistribution",
      "place-value pair",
      "adjacent elements",
      "first element"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0903.2555D"
    }
  }
}