{
  "id": "math/0303233",
  "version": "v3",
  "published": "2003-03-19T11:42:23.000Z",
  "updated": "2006-02-23T13:52:55.000Z",
  "title": "Algebraic Shifting and Basic Constructions on Simplicial Complexes",
  "authors": [
    "Eran Nevo"
  ],
  "comment": "Final version: 24 pages, no figures. Proof of Proposition 4.5 improved, minor changes",
  "journal": "J. Algeb. Combi., 22 (2005), 411-433",
  "categories": [
    "math.CO",
    "math.AC"
  ],
  "abstract": "We try to understand the behavior of exterior algebraic shifting with respect to basic constructions on simplicial complexes, like union and join. In particular we give a complete combinatorial description of the shifting of a disjoint union, and more generally of a union along a simplex, in terms of the shifting of its components. As a corollary, we prove the following, conjectured by Kalai: $\\Delta(K \\cup L) = \\Delta (\\Delta(K) \\cup \\Delta(L))$, where $K,L$ are complexes, $\\cup$ means disjoint union, and $\\Delta$ is the exterior shifting operator. We give an example showing that replacing the operation 'union' with the operation 'join' in the above equation is wrong, disproving a conjecture made by Kalai. We adopt a homological point of view on the algebraic shifting operator, which is used throughout this work.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2006-02-23T13:52:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E99",
      "13D99",
      "13F55"
    ],
    "keywords": [
      "basic constructions",
      "simplicial complexes",
      "complete combinatorial description",
      "means disjoint union",
      "exterior algebraic"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......3233N"
    }
  }
}