{
  "id": "math/0107162",
  "version": "v2",
  "published": "2001-07-23T14:37:07.000Z",
  "updated": "2003-08-13T20:44:02.000Z",
  "title": "Arithmetic properties of the adjacency matrix of quadriculated disks",
  "authors": [
    "Nicolau C. Saldanha",
    "Carlos Tomei"
  ],
  "comment": "12 pages, 9 figures",
  "categories": [
    "math.CO",
    "math.RA"
  ],
  "abstract": "Let $\\Delta$ be a bicolored quadriculated disk with black-to-white matrix $B_\\Delta$. We show how to factor $B_\\Delta = L\\tilde DU$, where $L$ and $U$ are lower and upper triangular matrices, $\\tilde D$ is obtained from a larger identity matrix by removing rows and columns and all entries of $L$, $\\tilde D$ and $U$ are equal to 0, 1 or -1.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2003-08-13T20:44:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B45",
      "05A15",
      "05C50",
      "05E05"
    ],
    "keywords": [
      "arithmetic properties",
      "adjacency matrix",
      "larger identity matrix",
      "upper triangular matrices",
      "black-to-white matrix"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math......7162S"
    }
  }
}