{
  "id": "2407.06550",
  "version": "v1",
  "published": "2024-07-09T05:14:27.000Z",
  "updated": "2024-07-09T05:14:27.000Z",
  "title": "Terwilliger Algebra of the Ordered Hamming Scheme",
  "authors": [
    "Yuta Watanabe"
  ],
  "comment": "22 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "This paper delves into the Terwilliger algebra associated with the ordered Hamming scheme, which extends from the wreath product of one-class association schemes and was initially introduced by Delsarte as a natural expansion of the Hamming schemes. Levstein, Maldonado and Penazzi have shown that the Terwilliger algebra of the Hamming scheme of length $n$ is the $n$-fold symmetric tensor algebra of that of the one-class association scheme. Furthermore, Bhattacharyya, Song and Tanaka have established that the Terwilliger algebra of the wreath product of a one-class association scheme is a direct sum of the ``primary'' subalgebra and commutative subalgebras. This paper extends these findings to encompass both conclusions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-09T05:14:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E30",
      "15A72",
      "33D50"
    ],
    "keywords": [
      "terwilliger algebra",
      "ordered hamming scheme",
      "one-class association scheme",
      "fold symmetric tensor algebra",
      "wreath product"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}