2024/08/12 by Sergey Kitaev, Dun Qiu, Kitaev, Sergey +1
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2408.05984
openalex publication_date 2024/08/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.