{
  "id": "1103.3363",
  "version": "v1",
  "published": "2011-03-17T09:24:04.000Z",
  "updated": "2011-03-17T09:24:04.000Z",
  "title": "Polynomial endomorphisms over finite fields: experimental results",
  "authors": [
    "Stefan Maubach",
    "Roel Willems"
  ],
  "comment": "15 pages",
  "categories": [
    "math.AG",
    "math.AC"
  ],
  "abstract": "Given a finite field $\\F_q$ and $n\\in \\N^*$, one could try to compute all polynomial endomorphisms $\\F_q^n\\lp \\F_q^n$ up to a certain degree with a specific property. We consider the case $n=3$. If the degree is low (like 2,3, or 4) and the finite field is small ($q\\leq 7$) then some of the computations are still feasible. In this article we study the following properties of endomorphisms: being a bijection of $\\F_q^n\\lp \\F_q^n$, being a polynomial automorphism, being a {\\em Mock automorphism}, and being a locally finite polynomial automorphism. In the resulting tables, we point out a few interesting objects, and pose some interesting conjectures which surfaced through our computations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-03-17T09:24:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite field",
      "polynomial endomorphisms",
      "experimental results",
      "locally finite polynomial automorphism",
      "computations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1103.3363M"
    }
  }
}