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<p>A De Bruijn cycle is a cyclic sequence in which every word of length <i>n</i> over an alphabet <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10623_2025_1609_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathcal {A}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">A</mi> </math></EquationSource> </InlineEquation> appears exactly once. De Bruijn tori are a two-dimensional analogue. Motivated by recent progress on universal partial cycles and words, which shorten De Bruijn cycles using a wildcard character, we introduce universal partial tori and matrices. We find them computationally and construct infinitely many of them using one-dimensional variants of universal cycles, including a new variant called a universal partial family.</p>

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Universal partial tori

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年3月27日

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  • William D. Carey,
  • Matthew David Kearney,
  • Rachel Kirsch,
  • Stefan Popescu

摘要

A De Bruijn cycle is a cyclic sequence in which every word of length n over an alphabet \(\mathcal {A}\) A appears exactly once. De Bruijn tori are a two-dimensional analogue. Motivated by recent progress on universal partial cycles and words, which shorten De Bruijn cycles using a wildcard character, we introduce universal partial tori and matrices. We find them computationally and construct infinitely many of them using one-dimensional variants of universal cycles, including a new variant called a universal partial family.