{
  "id": "math/0610482",
  "version": "v1",
  "published": "2006-10-16T12:45:46.000Z",
  "updated": "2006-10-16T12:45:46.000Z",
  "title": "A combinatorial reciprocity theorem for hyperplane arrangements",
  "authors": [
    "Christos A. Athanasiadis"
  ],
  "comment": "7 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Given a nonnegative integer $m$ and a finite collection ${\\mathcal A}$ of linear forms on ${\\mathbb Q}^d$, the arrangement of affine hyperplanes in ${\\mathbb Q}^d$ defined by the equations $\\alpha(x) = k$ for $\\alpha \\in {\\mathcal A}$ and integers $k \\in [-m, m]$ is denoted by ${\\mathcal A}^m$. It is proved that the coefficients of the characteristic polynomial of ${\\mathcal A}^m$ are quasi-polynomials in $m$ and that they satisfy a simple combinatorial reciprocity law.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-10-16T12:45:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52C35"
    ],
    "keywords": [
      "combinatorial reciprocity theorem",
      "hyperplane arrangements",
      "simple combinatorial reciprocity law",
      "characteristic polynomial",
      "finite collection"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....10482A"
    }
  }
}