{
  "id": "1008.0176",
  "version": "v1",
  "published": "2010-08-01T14:12:16.000Z",
  "updated": "2010-08-01T14:12:16.000Z",
  "title": "A Generalization of Plexes of Latin Squares",
  "authors": [
    "Kyle Pula"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "A $k$-plex of a latin square is a collection of cells representing each row, column, and symbol precisely $k$ times. The classic case of $k=1$ is more commonly known as a transversal. We introduce the concept of a $k$-weight, an integral weight function on the cells of a latin square whose row, column, and symbol sums are all $k$. We then show that several non-existence results about $k$-plexes can been seen as more general facts about $k$-weights and that the weight-analogues of several well-known existence conjectures for plexes actually hold for $k$-weights.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-08-01T14:12:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B15"
    ],
    "keywords": [
      "latin square",
      "generalization",
      "well-known existence conjectures",
      "integral weight function",
      "general facts"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1008.0176P"
    }
  }
}