{
  "id": "2105.10679",
  "version": "v1",
  "published": "2021-05-22T10:18:51.000Z",
  "updated": "2021-05-22T10:18:51.000Z",
  "title": "Tensor products of coherent configurations",
  "authors": [
    "Gang Chen",
    "Ilia Ponomarenko"
  ],
  "comment": "21 pages",
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "A Cartesian decomposition of a coherent configuration $\\cal X$ is defined as a special set of its parabolics that form a Cartesian decomposition of the underlying set. It turns out that every tensor decomposition of $\\cal X$ comes from a certain Cartesian decomposition. It is proved that if the coherent configuration $\\cal X$ is thick, then there is a unique maximal Cartesian decomposition of $\\cal X$, i.e., there is exactly one internal tensor decomposition of $\\cal X$ into indecomposable components. In particular, this implies an analog of the Krull--Schmidt theorem for the thick coherent configurations. A polynomial-time algorithm for finding the maximal Cartesian decomposition of a thick coherent configuration is constructed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-05-22T10:18:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E16",
      "05-08",
      "G.2.m"
    ],
    "keywords": [
      "tensor products",
      "thick coherent configuration",
      "unique maximal cartesian decomposition",
      "internal tensor decomposition",
      "special set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}