{
  "id": "2005.06354",
  "version": "v1",
  "published": "2020-05-13T15:00:49.000Z",
  "updated": "2020-05-13T15:00:49.000Z",
  "title": "$k$-arrangements, statistics and patterns",
  "authors": [
    "Shishuo Fu",
    "Guo-Niu Han",
    "Zhicong Lin"
  ],
  "comment": "25 pages, 1 figure and 1 table",
  "categories": [
    "math.CO"
  ],
  "abstract": "The $k$-arrangements are permutations whose fixed points are $k$-colored. We prove enumerative results related to statistics and patterns on $k$-arrangements, confirming several conjectures by Blitvi\\'c and Steingr\\'imsson. In particular, one of their conjectures regarding the equdistribution of the number of descents over the derangement form and the permutation form of $k$-arrangements is strengthened in two interesting ways. Moreover, as one application of the so-called Decrease Value Theorem, we calculate the generating function for a symmetric pair of Eulerian statistics over permutations arising in our study.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-13T15:00:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "arrangements",
      "decrease value theorem",
      "conjectures",
      "derangement form",
      "permutation form"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}