{
  "id": "0910.0533",
  "version": "v1",
  "published": "2009-10-03T10:19:10.000Z",
  "updated": "2009-10-03T10:19:10.000Z",
  "title": "Block-Transitive Designs in Affine Spaces",
  "authors": [
    "Michael Huber"
  ],
  "comment": "10 pages; to appear in: \"Designs, Codes and Cryptography\"",
  "categories": [
    "math.CO",
    "math.GR"
  ],
  "abstract": "This paper deals with block-transitive $t$-$(v,k,\\lambda)$ designs in affine spaces for large $t$, with a focus on the important index $\\lambda=1$ case. We prove that there are no non-trivial 5-$(v,k,1)$ designs admitting a block-transitive group of automorphisms that is of affine type. Moreover, we show that the corresponding non-existence result holds for 4-$(v,k,1)$ designs, except possibly when the group is one-dimensional affine. Our approach involves a consideration of the finite 2-homogeneous affine permutation groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-10-03T10:19:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "affine spaces",
      "block-transitive designs",
      "affine permutation groups",
      "corresponding non-existence result holds",
      "important index"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0910.0533H"
    }
  }
}