{
  "id": "2401.01687",
  "version": "v1",
  "published": "2024-01-03T11:46:03.000Z",
  "updated": "2024-01-03T11:46:03.000Z",
  "title": "Counting symmetric and non-symmetric peaks in a set partition",
  "authors": [
    "Walaa Asakly",
    "Noor Kezil"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "The aim of this paper is to derive explicit formulas for two distinct values. The first is the total number of symmetric peaks in a set partition of $[n]$ with exactly $k$ blocks, and the second one is the total number of non-symmetric peaks in a set partition of $[n]$ with exactly $k$ blocks. We represent these results in two ways. First by using the theory of generating functions, and the second by using combinatorial tools.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-03T11:46:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "set partition",
      "non-symmetric peaks",
      "counting symmetric",
      "total number",
      "distinct values"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}