{
  "id": "math/0211390",
  "version": "v1",
  "published": "2002-11-25T20:23:36.000Z",
  "updated": "2002-11-25T20:23:36.000Z",
  "title": "The cd-index of the Boolean lattice",
  "authors": [
    "Swapneel Mahajan"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We study some properties of the {\\bf cd}-index of the Boolean lattice. They are extremely similar to the properties of the {\\ab}-index, or equivalently, the flag $h$-vector of the Boolean lattice and hence may be viewed as their {\\bf cd}-analogues. We define a different algebra structure on the polynomial algebra $k < \\cv, \\dv>$ and give a derivation on this algebra. It is of significance for the Boolean lattice and forms our main tool. Using similar methods, we also prove some results for the {\\bf cd}-index of the cubical lattice. We show that the Dehn-Sommerville relations for the flag $f$-vector of an Eulerian poset are equivalent to certain simple identities that exist in our algebra.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-11-25T20:23:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A20",
      "06A11"
    ],
    "keywords": [
      "boolean lattice",
      "properties",
      "algebra structure",
      "polynomial algebra",
      "main tool"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math.....11390M"
    }
  }
}