{
  "id": "1210.7516",
  "version": "v1",
  "published": "2012-10-28T22:03:10.000Z",
  "updated": "2012-10-28T22:03:10.000Z",
  "title": "Even-freeness of cyclic 2-designs",
  "authors": [
    "Yuichiro Fujiwara"
  ],
  "comment": "12 pages, no figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "A Steiner 2-design of block size k is an ordered pair (V, B) of finite sets such that B is a family of k-subsets of V in which each pair of elements of V appears exactly once. A Steiner 2-design is said to be r-even-free if for every positive integer i =< r it contains no set of i elements of B in which each element of V appears exactly even times. We study the even-freeness of a Steiner 2-design when the cyclic group acts regularly on V. We prove the existence of infinitely many nontrivial Steiner 2-designs of large block size which have the cyclic automorphisms and higher even-freeness than the trivial lower bound but are not the points and lines of projective geometry.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-10-28T22:03:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B05",
      "05E18",
      "94B25"
    ],
    "keywords": [
      "trivial lower bound",
      "finite sets",
      "cyclic group acts",
      "block size"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.7516F"
    }
  }
}