{
  "id": "0903.2510",
  "version": "v1",
  "published": "2009-03-13T22:29:23.000Z",
  "updated": "2009-03-13T22:29:23.000Z",
  "title": "On the volume set of point sets in vector spaces over finite fields",
  "authors": [
    "Le Anh Vinh"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We show that if $\\mathcal{E}$ is a subset of the $d$-dimensional vector space over a finite field $\\mathbbm{F}_q$ ($d \\geq 3$) of cardinality $|\\mathcal{E}| \\geq (d-1)q^{d - 1}$, then the set of volumes of $d$-dimensional parallelepipeds determined by $\\mathcal{E}$ covers $\\mathbbm{F}_q$. This bound is sharp up to a factor of $(d-1)$ as taking $\\mathcal{E}$ to be a $(d - 1)$-hyperplane through the origin shows.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-03-13T22:29:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite field",
      "point sets",
      "volume set",
      "dimensional vector space",
      "cardinality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0903.2510V"
    }
  }
}