Scholarlink

<p>A universal cycle for <Emphasis Type="BoldItalic">k</Emphasis>-permutations is a cyclic arrangement in which each <Emphasis Type="BoldItalic">k</Emphasis>-permutation appears exactly once as <Emphasis Type="BoldItalic">k</Emphasis> consecutive elements. In this paper, we study the enumeration problem of universal cycles for <Emphasis Type="BoldItalic">k</Emphasis>-permutations (Problem 477 Jackson et al. Discrete Mathematics, <b>309</b>, 5341–5348, 2009) and obtain exact formulae for <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12095_2025_798_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="67" /> </InlineMediaObject> <EquationSource Format="TEX">\(\varvec{k=3, 4}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="bold-italic">k</mi> <mo mathvariant="bold">=</mo> <mn mathvariant="bold">3</mn> <mo mathvariant="bold">,</mo> <mn mathvariant="bold">4</mn> </mrow> </math></EquationSource> </InlineEquation>.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

An effective approach to enumerate universal cycles for k-permutations

  • 期刊论文

  • 发表日期：

    2025年4月28日

查看全文
  • Zuling Chang,
  • Qiang Wang,
  • Jie Xue

摘要

A universal cycle for k-permutations is a cyclic arrangement in which each k-permutation appears exactly once as k consecutive elements. In this paper, we study the enumeration problem of universal cycles for k-permutations (Problem 477 Jackson et al. Discrete Mathematics, 309, 5341–5348, 2009) and obtain exact formulae for \(\varvec{k=3, 4}\) k = 3 , 4 .