{
  "id": "math/0404320",
  "version": "v1",
  "published": "2004-04-18T19:45:27.000Z",
  "updated": "2004-04-18T19:45:27.000Z",
  "title": "Quadrangularity in Tournaments",
  "authors": [
    "J. Richard Lundgren",
    "Simone Severini",
    "Dustin J. Stewart"
  ],
  "comment": "13 pages",
  "categories": [
    "math.CO",
    "quant-ph"
  ],
  "abstract": "The pattern of a matrix M is a (0,1)-matrix which replaces all non-zero entries of M with a 1. There are several contexts in which studying the patterns of orthogonal matrices can be useful. One necessary condition for a matrix to be orthogonal is a property known as combinatorial orthogonality. If the adjacency matrix of a directed graph forms a pattern of a combinatorially orthogonal matrix, we say the digraph is quadrangular. We look at the quadrangular property in tournaments and regular tournaments.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-04-18T19:45:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C20",
      "05C50"
    ],
    "keywords": [
      "quadrangularity",
      "non-zero entries",
      "combinatorially orthogonal matrix",
      "quadrangular property",
      "orthogonal matrices"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......4320L"
    }
  }
}