{
  "id": "1507.02090",
  "version": "v1",
  "published": "2015-07-08T10:25:36.000Z",
  "updated": "2015-07-08T10:25:36.000Z",
  "title": "Exponential formulas for models of complex reflection groups",
  "authors": [
    "Giovanni Gaiffi"
  ],
  "categories": [
    "math.CO",
    "math.AT"
  ],
  "abstract": "In this paper we find some exponential formulas for the Betti numbers of the De Concini-Procesi minimal wonderful models Y_{G(r,p,n)} associated to the complex reflection groups G(r,p,n). Our formulas are different from the ones already known in the literature: they are obtained by a new combinatorial encoding of the elements of a basis of the cohomology by means of set partitions with weights and exponents. We also point out that a similar combinatorial encoding can be used to describe the faces of the real spherical wonderful models of type A_{n-1}=G(1,1,n), B_n=G(2,1,n) and D_n=G(2,2,n). This provides exponential formulas for the f-vectors of the associated nestohedra: the Stasheff's associahedra (in this case closed formulas are well known) and the graph associahedra of type D_n.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-07-08T10:25:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "complex reflection groups",
      "exponential formulas",
      "concini-procesi minimal wonderful models",
      "betti numbers",
      "stasheffs associahedra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}