{
  "id": "1510.03481",
  "version": "v1",
  "published": "2015-10-12T23:03:35.000Z",
  "updated": "2015-10-12T23:03:35.000Z",
  "title": "Incidences between planes over finite fields",
  "authors": [
    "Nguyen Duy Phuong",
    "Thang Pham",
    "Le Anh Vinh"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We use methods from spectral graph theory to obtain bounds on the number of incidences between $k$-planes and $h$-planes in $\\mathbb{F}_q^d$ which generalize a recent result given by Bennett, Iosevich, and Pakianathan (2014). More precisely, we prove that the number of incidences between a set $\\mathcal{P}$ of $k$-planes and a set $\\mathcal{H}$ of $h$-planes with $h\\ge 2k+1$, which is denoted by $I(\\mathcal{P},\\mathcal{H})$, satisfies \\[\\left\\vert I(\\mathcal{P},\\mathcal{H})-\\frac{|\\mathcal{P}||\\mathcal{H}|}{q^{(d-h)(k+1)}}\\right\\vert \\lesssim q^{\\frac{(d-h)h+k(2h-d-k+1)}{2}}\\sqrt{|\\mathcal{P}||\\mathcal{H}|}. \\]",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-12T23:03:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite fields",
      "incidences",
      "spectral graph theory",
      "pakianathan"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151003481D"
    }
  }
}