{
  "id": "1811.03892",
  "version": "v1",
  "published": "2018-11-09T13:32:47.000Z",
  "updated": "2018-11-09T13:32:47.000Z",
  "title": "Graded Betti numbers of balanced simplicial complexes",
  "authors": [
    "Martina Juhnke-Kubitzke",
    "Lorenzo Venturello"
  ],
  "comment": "33 pages, 3 figures",
  "categories": [
    "math.CO",
    "math.AC"
  ],
  "abstract": "We prove upper bounds for the graded Betti numbers of Stanley-Reisner rings of balanced simplicial complexes. Along the way we show bounds for Cohen-Macaulay graded rings $S/I$, where $S$ is a polynomial ring and $I\\subseteq S$ is an homogeneous ideal containing a certain number of generators in degree 2, including the squares of the variables. Using similar techniques we provide upper bounds for the number of linear syzygies for Stanley-Reisner of balanced normal pseudomanifolds. Moreover, we compute explicitly the graded Betti numbers of cross-polytopal stacked spheres, and show that they only depend on the dimension and the number of vertices, rather than also the combinatorial type.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-09T13:32:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E45",
      "05E40",
      "13F55"
    ],
    "keywords": [
      "graded betti numbers",
      "balanced simplicial complexes",
      "upper bounds",
      "stanley-reisner rings",
      "cohen-macaulay graded rings"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}