{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:38:41Z","timestamp":1753889921851,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","issue":"Combinatorics","license":[{"start":{"date-parts":[[2017,5,31]],"date-time":"2017-05-31T00:00:00Z","timestamp":1496188800000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"},{"start":{"date-parts":[[2017,5,31]],"date-time":"2017-05-31T00:00:00Z","timestamp":1496188800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"},{"start":{"date-parts":[[2017,5,31]],"date-time":"2017-05-31T00:00:00Z","timestamp":1496188800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2025,3,31]]},"abstract":"<jats:p>A universal word for a finite alphabet $A$ and some integer $n\\geq 1$ is a word over $A$ such that every word in $A^n$ appears exactly once as a subword (cyclically or linearly). It is well-known and easy to prove that universal words exist for any $A$ and $n$. In this work we initiate the systematic study of universal partial words. These are words that in addition to the letters from $A$ may contain an arbitrary number of occurrences of a special `joker' symbol $\\Diamond\\notin A$, which can be substituted by any symbol from $A$. For example, $u=0\\Diamond 011100$ is a linear partial word for the binary alphabet $A=\\{0,1\\}$ and for $n=3$ (e.g., the first three letters of $u$ yield the subwords $000$ and $010$). We present results on the existence and non-existence of linear and cyclic universal partial words in different situations (depending on the number of $\\Diamond$s and their positions), including various explicit constructions. We also provide numerous examples of universal partial words that we found with the help of a computer.<\/jats:p>","DOI":"10.23638\/dmtcs-19-1-16","type":"journal-article","created":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T16:39:47Z","timestamp":1743698387000},"source":"Crossref","is-referenced-by-count":0,"title":["On universal partial words"],"prefix":"10.23638","volume":"Vol. 19 no. 1","author":[{"given":"Herman Z. Q.","family":"Chen","sequence":"first","affiliation":[]},{"given":"Sergey","family":"Kitaev","sequence":"additional","affiliation":[]},{"given":"Torsten","family":"M\u00fctze","sequence":"additional","affiliation":[]},{"given":"Brian Y.","family":"Sun","sequence":"additional","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2017,5,31]]},"container-title":["Discrete Mathematics &amp; Theoretical Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/1601.06456v4","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/1601.06456v4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T16:39:47Z","timestamp":1743698387000},"score":1,"resource":{"primary":{"URL":"http:\/\/dmtcs.episciences.org\/2205"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,5,31]]},"references-count":0,"journal-issue":{"issue":"Combinatorics","published-online":{"date-parts":[[2017,5,31]]}},"URL":"https:\/\/doi.org\/10.23638\/dmtcs-19-1-16","relation":{"has-preprint":[{"id-type":"arxiv","id":"1601.06456v2","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"1601.06456","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1601.06456","asserted-by":"subject"}]},"ISSN":["1365-8050"],"issn-type":[{"type":"electronic","value":"1365-8050"}],"subject":[],"published":{"date-parts":[[2017,5,31]]},"article-number":"2205"}}