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Universal partial tori
William D. Carey, Matthew David Kearney, Rachel Kirsch, Stefan Popescu
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A De Bruijn cycle is a cyclic sequence in which every word of length n over an alphabet 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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