On a family of universal cycles for multi-dimensional permutations
Kitaev, Sergey and Qiu, Dun (2024) On a family of universal cycles for multi-dimensional permutations. Discrete Applied Mathematics, 359. pp. 310-320. ISSN 0166-218X
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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.
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Item type: Article ID code: 90224 Dates: DateEvent31 December 2024Published24 August 2024Published Online12 August 2024Accepted29 November 2023SubmittedSubjects: Science > Mathematics
History General and Old World > SpainDepartment: Faculty of Science > Mathematics and Statistics Depositing user: Pure Administrator Date deposited: 13 Aug 2024 14:09 Last modified: 26 Aug 2024 11:38 Related URLs: URI: https://strathprints.strath.ac.uk/id/eprint/90224