Universal Partial Words over Non-Binary Alphabets
arXiv:1611.03928 · doi:10.1016/j.tcs.2017.12.022
Abstract
Chen, Kitaev, Mütze, 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 , 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 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.
14 pages, submitted version