{
  "id": "1409.3869",
  "version": "v1",
  "published": "2014-09-12T21:28:19.000Z",
  "updated": "2014-09-12T21:28:19.000Z",
  "title": "Selections Without Adjacency on a Rectangular Grid",
  "authors": [
    "Jacob A. Siehler"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Using T(m,n;k) to denote the number of ways to make a selection of k squares from an (m x n) rectangular grid with no two squares in the selection adjacent, we give a formula for T(2,n;k), prove some identities satisfied by these numbers, and show that T(2,n;k) is given by a degree k polynomial in n. We give simple formulas for the first few (most significant) coefficients of the polynomials. We give corresponding results for T(3,n;k) as well. Finally we prove a unimodality theorem which shows, in particular, how to choose k in order to maximize T(2,n;k).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-09-12T21:28:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A15"
    ],
    "keywords": [
      "rectangular grid",
      "polynomial",
      "selection adjacent",
      "simple formulas",
      "unimodality theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1409.3869S"
    }
  }
}