{
  "id": "1605.00813",
  "version": "v1",
  "published": "2016-05-03T09:36:28.000Z",
  "updated": "2016-05-03T09:36:28.000Z",
  "title": "On certain recurrent and automatic sequences in finite fields",
  "authors": [
    "Alain Lasjaunias",
    "Jia-Yan Yao"
  ],
  "comment": "10 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this work we extend our study on a link between automaticity and certain algebraic power series over finite fields. Our starting point is a family of sequences in a finite field of characteristic $2$, recently introduced by the first author in connection with algebraic continued fractions. By including it in a large family of recurrent sequences in an arbitrary finite field, we prove its automaticity. Then we give a criterion on automatic sequences, generalizing a previous result and this allows us to present new families of automatic sequences in an arbitrary finite field.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-03T09:36:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11J70",
      "11T55",
      "11B85"
    ],
    "keywords": [
      "automatic sequences",
      "arbitrary finite field",
      "algebraic power series",
      "automaticity",
      "algebraic continued fractions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}