{
  "id": "0811.1983",
  "version": "v1",
  "published": "2008-11-12T20:57:26.000Z",
  "updated": "2008-11-12T20:57:26.000Z",
  "title": "Differential posets and Smith normal forms",
  "authors": [
    "Alexander Miller",
    "Victor Reiner"
  ],
  "comment": "29 pages, 9 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "We conjecture a strong property for the up and down maps U and D in an r-differential poset: DU+tI and UD+tI have Smith normal forms over Z[t]. In particular, this would determine the integral structure of the maps U, D, UD, DU, including their ranks in any characteristic. As evidence, we prove the conjecture for the Young-Fibonacci lattice YF studied by Okada and its r-differential generalizations Z(r), as well as verifying many of its consequences for Young's lattice Y and the r-differential Cartesian products Y^r.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-11-12T20:57:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E99"
    ],
    "keywords": [
      "smith normal forms",
      "differential posets",
      "young-fibonacci lattice yf",
      "r-differential cartesian products",
      "strong property"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0811.1983M"
    }
  }
}