{
  "id": "2408.07646",
  "version": "v1",
  "published": "2024-08-14T16:17:51.000Z",
  "updated": "2024-08-14T16:17:51.000Z",
  "title": "Topology of total cut and cut complexes of grid graphs",
  "authors": [
    "Himanshu Chandrakar",
    "Nisith Ranjan Hazra",
    "Debotosh Rout",
    "Anurag Singh"
  ],
  "comment": "25 pages, 11 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "Inspired by the work of Fr\\\"oberg (1990) and Eagon and Reiner (1998), Bayer et al. recently introduced two new graph complexes: total cut complexes and cut complexes. In this article, we investigate these complexes specifically for (rectangular) grid graphs, focusing on $2 \\times n$ and $3 \\times n$ cases. We extend and refine the work of Bayer et al., proving and strengthening several of their conjectures, thereby enhancing the understanding of the topological and combinatorial properties of these graph complexes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-14T16:17:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "grid graphs",
      "graph complexes",
      "total cut complexes",
      "combinatorial properties",
      "rectangular"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}