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تسجيل مستخدم جديدUniversal Partial Words over Non-Binary Alphabets
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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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