{
  "id": "1402.6146",
  "version": "v2",
  "published": "2014-02-25T12:21:06.000Z",
  "updated": "2014-03-25T11:58:30.000Z",
  "title": "An Identity of Distributive Lattices",
  "authors": [
    "Himadri Mukherjee"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "In a finite distributive lattice $\\L$ we define two functions $s(\\alpha)=|\\{\\delta \\in \\mathcal{L} | \\delta \\leq \\alpha \\}|$ and $l(\\alpha)=|\\{\\delta \\in \\mathcal{L} | \\delta \\geq \\alpha \\}|$. In this present article we prove that the sum of these two functions over a finite distributive lattice are equal. Using this identity we give a formula for the number of non-comparable pairs of elements in a finite distributive lattice.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-03-25T11:58:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite distributive lattice",
      "non-comparable pairs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1402.6146M"
    }
  }
}