{
  "id": "2404.01783",
  "version": "v1",
  "published": "2024-04-02T09:45:49.000Z",
  "updated": "2024-04-02T09:45:49.000Z",
  "title": "Synchronicity of descent and excedance enumerators in the alternating subgroup",
  "authors": [
    "Umesh Shankar"
  ],
  "comment": "Comments are welcome!",
  "categories": [
    "math.CO"
  ],
  "abstract": "Generalising the work of Dey, we define the notion of ultra-synchronicity of sequences of real numbers. Let $B_{n,k},C_{n,k},P_{n,k},Q_{n,k}$ be the number of even permutations with $k$ descents, odd permutations with $k$ descents, even permutations with $k$ excedances and odd permutations with $k$ excedances respectively. We show that the four sequences are ultra-synchronised for all $n\\ge 5$. This proves a strengthening of two conjectures of Dey.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-04-02T09:45:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A05",
      "05A20"
    ],
    "keywords": [
      "excedance enumerators",
      "alternating subgroup",
      "odd permutations",
      "real numbers",
      "ultra-synchronicity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}