{
  "id": "1405.3001",
  "version": "v2",
  "published": "2014-05-12T23:50:32.000Z",
  "updated": "2016-09-08T02:09:29.000Z",
  "title": "A $q$-Queens Problem. V. The Bishops' Period",
  "authors": [
    "Thomas Zaslavsky",
    "Seth Chaiken",
    "Christopher R. H. Hanusa"
  ],
  "comment": "15 pp.; 12 pp. without white space. v2: Updated citations, rearranged authors. 12 pp",
  "categories": [
    "math.CO"
  ],
  "abstract": "Part I showed that the number of ways to place $q$ nonattacking queens or similar chess pieces on an $n\\times n$ square chessboard is a quasipolynomial function of $n$. We prove the previously empirically observed period of the bishops quasipolynomial, which is exactly 2 for three or more bishops. The proof depends on signed graphs and the Ehrhart theory of inside-out polytopes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-05-12T23:50:32.000Z",
      "comment": "15 pp.; 12 pp. without white space",
      "journal": null,
      "doi": null,
      "authors": [
        "Seth Chaiken",
        "Christopher R. H. Hanusa",
        "Thomas Zaslavsky"
      ]
    },
    {
      "version": "v2",
      "updated": "2016-09-08T02:09:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A15",
      "00A08",
      "05C22",
      "52C07",
      "52C35"
    ],
    "keywords": [
      "queens problem",
      "similar chess pieces",
      "ehrhart theory",
      "proof depends",
      "bishops quasipolynomial"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.3001C"
    }
  }
}