{
  "id": "2410.24044",
  "version": "v1",
  "published": "2024-10-31T15:39:40.000Z",
  "updated": "2024-10-31T15:39:40.000Z",
  "title": "Partial Algebraic Shifting",
  "authors": [
    "Antony Della Vecchia",
    "Michael Joswig",
    "Fabian Lenzen"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We study algebraic shifting of uniform hypergraphs and finite simplicial complexes in the exterior algebra with respect to matrices which are not necessarily generic. Several questions raised by Kalai (2002) are addressed. For instance, it turns out that the combinatorial shifting of Erd\\H{o}s$\\unicode{x2013}$Ko$\\unicode{x2013}$Rado (1961) arises as a special case. Moreover, we identify a sufficient condition for partial shifting to preserve the Betti numbers of a simplicial complex; examples show that this condition is sharp.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-31T15:39:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E45",
      "13D99",
      "20G99",
      "05C35"
    ],
    "keywords": [
      "partial algebraic shifting",
      "finite simplicial complexes",
      "study algebraic",
      "exterior algebra",
      "uniform hypergraphs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}