{
  "id": "1410.3147",
  "version": "v1",
  "published": "2014-10-12T20:47:01.000Z",
  "updated": "2014-10-12T20:47:01.000Z",
  "title": "Linear bounds on matrix extremal functions using visibility hypergraphs",
  "authors": [
    "Jesse Geneson",
    "Lilly Shen"
  ],
  "comment": "11 pages, 4 figures",
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "The 0-1 matrix A contains a 0-1 matrix M if some submatrix of A can be transformed into M by changing some ones to zeroes. If A does not contain M, then A avoids M. Let ex(n,M) be the maximum number of ones in an n x n 0-1 matrix that avoids M, and let ex_k(m,M) be the maximum number of columns in a 0-1 matrix with m rows that avoids M and has at least k ones in every column. A method for bounding ex(n,M) by using bounds on the maximum number of edges in bar visibility graphs was introduced in (R. Fulek, Discrete Mathematics 309, 2009). By using a similar method with bar visibility hypergraphs, we obtain linear bounds on the extremal functions of other forbidden 0-1 matrices.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-12T20:47:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05D99"
    ],
    "keywords": [
      "matrix extremal functions",
      "linear bounds",
      "maximum number",
      "bar visibility hypergraphs",
      "bar visibility graphs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1410.3147G"
    }
  }
}