{
  "id": "1104.5168",
  "version": "v3",
  "published": "2011-04-27T15:52:21.000Z",
  "updated": "2011-11-16T03:46:00.000Z",
  "title": "Neighborliness of the symmetric moment curve",
  "authors": [
    "Alexander Barvinok",
    "Seung Jin Lee",
    "Isabella Novik"
  ],
  "comment": "28 pages, proofs are simplified and results are strengthened somewhat",
  "doi": "10.1112/S0025579312000010",
  "categories": [
    "math.MG",
    "math.CO"
  ],
  "abstract": "We consider the convex hull B_k of the symmetric moment curve U(t)=(cos t, sin t, cos 3t, sin 3t, ..., cos (2k-1)t, sin (2k-1)t) in R^{2k}, where t ranges over the unit circle S= R/2pi Z. The curve U(t) is locally neighborly: as long as t_1, ..., t_k lie in an open arc of S of a certain length phi_k>0, the convex hull of the points U(t_1), ..., U(t_k) is a face of B_k. We characterize the maximum possible length phi_k, proving, in particular, that phi_k > pi/2 for all k and that the limit of phi_k is pi/2 as k grows. This allows us to construct centrally symmetric polytopes with a record number of faces.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-11-16T03:46:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52A20",
      "52B12",
      "26C10"
    ],
    "keywords": [
      "symmetric moment curve",
      "neighborliness",
      "convex hull",
      "construct centrally symmetric polytopes",
      "cos 3t"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1104.5168B"
    }
  }
}