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On shortening $$u$$-cycles and $$u$$-words for permutations. (English) Zbl 1409.05010
Summary: 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 $$k = 0, 1, \ldots,(n - 2)!$$.

##### MSC:
 05A05 Permutations, words, matrices
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##### References:
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