{
  "id": "2309.14128",
  "version": "v1",
  "published": "2023-09-25T13:29:20.000Z",
  "updated": "2023-09-25T13:29:20.000Z",
  "title": "Symmetry of $f$-vectors of toric arrangements in general position and some applications",
  "authors": [
    "Diana Bergerová"
  ],
  "comment": "19 pages, 9 figures; all comments welcome",
  "categories": [
    "math.CO"
  ],
  "abstract": "A toric hyperplane is the preimage of a point $x \\in S^1$ of a continuous surjective group homomorphism $\\theta: \\mathbb{T}^n \\to S^1$. A finite hyperplane arrangement is a finite collection of such hyperplanes. In this paper, we study the combinatorial properties of finite hyperplane arrangements on $\\mathbb{T}^n$ which are spanning and in general position. Specifically, we describe the symmetry of $f$-vectors arising in such arrangements and a few applications of the result to count configurations of hyperplanes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-25T13:29:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "general position",
      "toric arrangements",
      "finite hyperplane arrangement",
      "applications",
      "toric hyperplane"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}