{
  "id": "2408.05984",
  "version": "v1",
  "published": "2024-08-12T08:19:41.000Z",
  "updated": "2024-08-12T08:19:41.000Z",
  "title": "On a family of universal cycles for multi-dimensional permutations",
  "authors": [
    "Sergey Kitaev",
    "Dun Qiu"
  ],
  "comment": "To appear in Discrete Applied Mathematics",
  "categories": [
    "math.CO"
  ],
  "abstract": "A universal cycle (u-cycle) for permutations of length $n$ is a cyclic word, any size $n$ window of which is order-isomorphic to exactly one permutation of length $n$, and all permutations of length $n$ are covered. It is known that u-cycles for permutations exist, and they have been considered in the literature in several papers from different points of view. In this paper, we show how to construct a family of u-cycles for multi-dimensional permutations, which is based on applying an appropriate greedy algorithm. Our construction is a generalisation of the greedy way by Gao et al. to construct u-cycles for permutations. We also note the existence of u-cycles for $d$-dimensional matrices.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-12T08:19:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "multi-dimensional permutations",
      "universal cycle",
      "appropriate greedy algorithm",
      "construct u-cycles",
      "greedy way"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}