{
  "id": "1610.09868",
  "version": "v1",
  "published": "2016-10-31T11:11:57.000Z",
  "updated": "2016-10-31T11:11:57.000Z",
  "title": "On ranks of regular polygons",
  "authors": [
    "António Pedro Goucha",
    "João Gouveia",
    "Pedro M. Silva"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper we study various versions of extension complexity for polygons through the study of factorization ranks of their slack matrices. In particular, we develop a new asymptotic lower bound for their nonnegative rank, shortening the gap between the current bounds, we introduce a new upper bound for their boolean rank, deriving from it some new numerical results, and we study their complex semidefinite rank, uncovering the possibility of non monotonicity of the ranks of regular $n$-gons.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-31T11:11:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "regular polygons",
      "complex semidefinite rank",
      "asymptotic lower bound",
      "upper bound",
      "slack matrices"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}