论文标题
缩短了通用周期的排列
Shortened universal cycles for permutations
论文作者
论文摘要
Kitaev，Potapov和Vajnovszki [在缩短U-Cycles和U-Words以进行排列的U-Words，离散应用。 Math，2019年]描述了如何缩短通用单词的排列单词，以介绍不可比拟的元素，以缩短$ n！+n！+n！+n！+n！+n！+n！+n！他们推测，也可以使用无与伦比的元素缩短通用周期的排列，以缩短$ n！-i（n-1）$的$ i（n-1）$，用于[（n-2）！] $。在本说明中，我们证明了他们的猜想。证明是建设性的，在途中，我们还展示了一种构造通用周期排列的新方法。
Kitaev, Potapov, and Vajnovszki [On shortening u-cycles and u-words for permutations, Discrete Appl. Math, 2019] described how to shorten universal words for permutations, to length $n!+n-1-i(n-1)$ for any $i \in [(n-2)!]$, by introducing incomparable elements. They conjectured that it is also possible to use incomparable elements to shorten universal cycles for permutations to length $n!-i(n-1)$ for any $i \in [(n-2)!]$. In this note we prove their conjecture. The proof is constructive, and, on the way, we also show a new method for constructing universal cycles for permutations.
