Universal cycles are generalizations of de Bruijn cycles and Gray codes thatwere introduced originally by Chung, Diaconis, and Graham in 1992. They havebeen developed by many authors since, for various combinatorial objects such asstrings, subsets, permutations, partitions, vector spaces, and designs. Onegeneralization of universal cycles, which require almost complete overlap ofconsecutive words, is $s$-overlap cycles, which relax such a constraint. Inthis paper we study permutations and some closely related class of strings,namely juggling sequences and functions. We prove the existence of $s$-overlapcycles for these objects, as they do not always lend themselves to theuniversal cycle structure.
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机译：通用循环是de Bruijn循环和Gray代码的泛化，它们最初由Chung，Diaconis和Graham于1992年引入。此后由许多作者开发，适用于各种组合对象，例如字符串，子集，置换，分区，向量空间和设计。通用循环的一个一般化，即几乎连续的连续词重叠，是$ s $重叠循环，它放宽了这种约束。在本文中，我们研究了排列和一些紧密相关的字符串类别，即杂耍序列和功能。我们证明了这些对象存在$ s $ -overcycles，因为它们并不总是适合于通用周期结构。
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