On shortening u-cycles and u-words for permutations

Kitaev, Sergey and Potapov, Vladimir N. and Vajnovszki, Vincent (2019) On shortening u-cycles and u-words for permutations. Discrete Applied Mathematics, 260. pp. 203-213. ISSN 0166-218X

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    Abstract

    This paper initiates the study of shortening universal cycles (u-cycles) and universal words (u-words) for permutations either by using incomparable elements, or by using non-deterministic symbols. The latter approach is similar in nature to the recent relevant studies for the de Bruijn sequences. A particular result we obtain in this paper is that u-words for n-permutations exist of lengths n!+(1−k)(n−1) for k=0,1,…,(n−2)!.