On a family of universal cycles for multi-dimensional permutations
Sergey Kitaev, Dun Qiu · Discrete Applied Mathematics · 2024
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 generalization 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.