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arXiv · 1611.03928

Universal Partial Words over Non-Binary Alphabets

Bennet Goeckner·Corbin Groothuis·Cyrus Hettle·Brian Kell·Pamela Kirkpatrick·Rachel Kirsch·Ryan Solava
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Abstract

Chen, Kitaev, M\"{u}tze, and Sun recently introduced the notion of universal partial words, a generalization of universal words and de Bruijn sequences. Universal partial words allow for a wild-card character $\diamond$, which is a placeholder for any letter in the alphabet. We settle and strengthen conjectures posed in the same paper where this notion was introduced. For non-binary alphabets, we show that universal partial words have periodic $\diamond$ structure and are cyclic, and we give number-theoretic conditions on the existence of universal partial words. In addition, we provide an explicit construction for a family of universal partial words over alphabets of even size.

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Bennet Goeckner, Corbin Groothuis, Cyrus Hettle, Brian Kell, Pamela Kirkpatrick, Rachel Kirsch, Ryan Solava. 2016-11-12. Universal Partial Words over Non-Binary Alphabets. https://doi.org/10.1016/j.tcs.2017.12.022

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