{
  "id": "1407.2823",
  "version": "v1",
  "published": "2014-07-10T15:11:46.000Z",
  "updated": "2014-07-10T15:11:46.000Z",
  "title": "On Aperiodic Subtraction Games with Bounded Nim Sequence",
  "authors": [
    "Nathan Fox"
  ],
  "comment": "45 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Subtraction games are a class of impartial combinatorial games whose positions correspond to nonnegative integers and whose moves correspond to subtracting one of a fixed set of numbers from the current position. Though they are easy to define, sub- traction games have proven difficult to analyze. In particular, few general results about their Sprague-Grundy values are known. In this paper, we construct an example of a subtraction game whose sequence of Sprague-Grundy values is ternary and aperiodic, and we develop a theory that might lead to a generalization of our construction.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-10T15:11:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "91A46",
      "68R15",
      "05A19"
    ],
    "keywords": [
      "aperiodic subtraction games",
      "bounded nim sequence",
      "sprague-grundy values",
      "impartial combinatorial games",
      "moves correspond"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 45,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.2823F"
    }
  }
}