{
  "id": "2401.12839",
  "version": "v1",
  "published": "2024-01-23T15:19:32.000Z",
  "updated": "2024-01-23T15:19:32.000Z",
  "title": "Hamilton cycles for involutions of classical types",
  "authors": [
    "Gonçalo Gutierres",
    "Ricardo Mamede",
    "José Luis Santos"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Let ${\\mathcal W}_n$ denote any of the three families of classical Weyl groups: the symmetric groups ${\\mathcal S}_n$, the hyperoctahedral groups (signed permutation groups) ${\\mathcal S}^B_n$, or the even-signed permutation groups ${\\mathcal S}^D_n$. In this paper we give an uniform construction of a Hamilton cycle for the restriction to involutions on these three families of groups with respect to a inverse-closed connecting set of involutions. This Hamilton cycle is optimal with respect to the Hamming distance only for the symmetric group ${\\mathcal S}_n$. We also recall an optimal algorithm for a Gray code for type $B$ involutions. A modification of this algorithm would provide a Gray Code for type $D$ involutions with Hamming distance two, which would be optimal. We give such a construction for ${\\mathcal S}^D_4$ and ${\\mathcal S}^D_5$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-23T15:19:32.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hamilton cycle",
      "involutions",
      "classical types",
      "symmetric group",
      "gray code"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}