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arXiv · 2409.12417

Universal partial tori

William D. Carey·Matthew David Kearney·Rachel Kirsch·Stefan Popescu
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Abstract

A De Bruijn cycle is a cyclic sequence in which every word of length $n$ over an alphabet $\mathcal{A}$ 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.

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William D. Carey, Matthew David Kearney, Rachel Kirsch, Stefan Popescu. 2025-03-31. Universal partial tori. https://doi.org/10.1007/s10623-025-01609-9

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