{
  "id": "2008.01044",
  "version": "v1",
  "published": "2020-08-03T17:31:19.000Z",
  "updated": "2020-08-03T17:31:19.000Z",
  "title": "The Partition Complex: an invitation to combinatorial commutative algebra",
  "authors": [
    "Karim Adiprasito",
    "Geva Yashfe"
  ],
  "comment": "45 pages",
  "categories": [
    "math.CO",
    "math.AC",
    "math.AG"
  ],
  "abstract": "We provide a new foundation for combinatorial commutative algebra and Stanley-Reisner theory using the partition complex introduced in [Adi18]. One of the main advantages is that it is entirely self-contained, using only a minimal knowledge of algebra and topology. On the other hand, we also develop new techniques and results using this approach. In particular, we provide - A novel, self-contained method of establishing Reisner's theorem and Schenzel's formula for Buchsbaum complexes. - A simple new way to establish Poincar\\'e duality for face rings of manifolds, in much greater generality and precision than previous treatments. - A \"master-theorem\" to generalize several previous results concerning the Lefschetz theorem on subdivisions. - Proof for a conjecture of K\\\"uhnel concerning triangulated manifolds with boundary.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-03T17:31:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "combinatorial commutative algebra",
      "partition complex",
      "invitation",
      "lefschetz theorem",
      "greater generality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 45,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}