{
  "id": "0706.1529",
  "version": "v1",
  "published": "2007-06-11T17:55:34.000Z",
  "updated": "2007-06-11T17:55:34.000Z",
  "title": "On multipartite posets",
  "authors": [
    "Geir Agnarsson"
  ],
  "comment": "6 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "A poset $\\mathbf{P} = (X,\\preceq)$ is {\\em $m$-partite} if $X$ has a partition $X = X_1 \\cup ... \\cup X_m$ such that (1) each $X_i$ forms an antichain in $\\mathbf{P}$, and (2) $x\\prec y$ implies $x\\in X_i$ and $y\\in X_j$ where $i<j$. In this article we derive a tight asymptotic upper bound on the order dimension of $m$-partite posets in terms of $m$ and their bipartite sub-posets in a constructive and elementary way.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-06-11T17:55:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "06A07"
    ],
    "keywords": [
      "multipartite posets",
      "tight asymptotic upper bound",
      "order dimension",
      "bipartite sub-posets",
      "elementary way"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0706.1529A"
    }
  }
}