{
  "id": "2102.11277",
  "version": "v1",
  "published": "2021-02-20T20:51:45.000Z",
  "updated": "2021-02-20T20:51:45.000Z",
  "title": "Ricci curvature, Bruhat graphs and Coxeter groups",
  "authors": [
    "Viola Siconolfi"
  ],
  "comment": "13 pages. arXiv admin note: text overlap with arXiv:2102.10134",
  "categories": [
    "math.CO",
    "math.GR"
  ],
  "abstract": "We consider the notion of discrete Ricci curvature for graphs defined by Schmuckenschl{\\\"a}ger \\cite{shmuck} and compute its value for Bruhat graphs associated to finite Coxeter groups. To do so we work with the geometric realization of a finite Coxeter group and a classical result obtained by Dyer in \\cite{Dyer}. As an applications we obtain a bound for the spectral gap of the Bruhat graph of any finite Coxeter group and an isoperimetric inequality for them. Our proofs are case-free.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-20T20:51:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F55",
      "53A70",
      "05C50"
    ],
    "keywords": [
      "bruhat graph",
      "finite coxeter group",
      "discrete ricci curvature",
      "geometric realization",
      "spectral gap"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}