On shortening u-cycles and u-words for permutations

Sergey Kitaev, Vladimir N. Potapov, Vincent Vajnovszki

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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)!.

Original languageEnglish
Pages (from-to)203-213
Number of pages11
JournalDiscrete Applied Mathematics
Early online date6 Feb 2019
Publication statusPublished - 15 May 2019


  • universal cycles
  • universal words
  • permutations
  • mathematics
  • computation


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