Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Universal Partial Words over Non-Binary Alphabets   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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The categories of this paper are: hep-lat
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The categories of this paper are: funct-an
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The categories of this paper are: stat
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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
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The categories of this paper are: physics
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The categories of this paper are: nlin
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The categories of this paper are: quant-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-ex