Shortened universal cycles for permutations

被引：0

作者：

Kirsch, Rachel ^{[1
]}

Lidicky, Bernard ^{[2
]}

Sibley, Clare ^{[3
]}

Sprangel, Elizabeth ^{[2
]}

机构：

[1] George Mason Univ, Dept Math Sci, Fairfax, VA 22030 USA

[2] Iowa State Univ, Dept Math, Ames, IA USA

[3] Rice Univ, Houston, TX USA

来源：

DISCRETE APPLIED MATHEMATICS | 2023年 / 324卷

关键词：

Universal cycles; Permutation; Compression; DE-BRUIJN SEQUENCES; WORDS;

D O I：

10.1016/j.dam.2022.09.026

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Kitaev et al. (2019) described how to shorten universal words for permutations, to length n! + n - 1 - i(n - 1) for any i is an element of [(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 is an element of [(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.(c) 2022 Elsevier B.V. All rights reserved.

引用

页码：219 / 228

页数：10

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