{
  "id": "2109.09773",
  "version": "v1",
  "published": "2021-09-20T18:04:33.000Z",
  "updated": "2021-09-20T18:04:33.000Z",
  "title": "A note on fully commutative elements in complex reflection groups",
  "authors": [
    "Jiayuan Wang"
  ],
  "comment": "14 pages, 7 tables. Comments are welcome!",
  "categories": [
    "math.CO"
  ],
  "abstract": "Fully commutative elements in types $B$ and $D$ are completely characterized and counted by Stembridge. Recently, Feinberg-Kim-Lee-Oh have extended the study of fully commutative elements from Coxeter groups to the complex setting, giving an enumeration of such elements in $G(m,1,n)$. In this note, we prove a connection between fully commutative elements in $B_n$ and in $G(m,1,n)$, which allows us to characterize fully commutative elements in $G(m,1,n )$ by pattern avoidance. Further, we present a counting formula for such elements in $G(m,1,n)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-09-20T18:04:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "complex reflection groups",
      "coxeter groups",
      "stembridge",
      "feinberg-kim-lee-oh",
      "enumeration"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}