{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T15:05:22Z","timestamp":1773241522716,"version":"3.50.1"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>We present a class of languages that have an interesting property: For each language $\\mathbf{L}$ in the class, both the classic greedy algorithm and the classic Lyndon word (or necklace) concatenation algorithm provide the lexicographically smallest universal cycle for $\\mathbf{L}$. The languages consist of length $n$ strings over $\\{1,2,\\ldots ,k\\}$ that are closed under rotation with their subset of necklaces also being closed under replacing any suffix of length $i$ by $i$ copies of $k$. Examples include all strings (in which case universal cycles are commonly known as de Bruijn sequences), strings that sum to at least $s$, strings with at most $d$ cyclic descents for a fixed $d&gt;0$, strings with at most $d$ cyclic decrements for a fixed $d&gt;0$, and strings avoiding a given period. Our class is also closed under both union and intersection, and our results generalize results of several previous papers.<\/jats:p>","DOI":"10.37236\/5517","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T21:57:58Z","timestamp":1578693478000},"source":"Crossref","is-referenced-by-count":14,"title":["Generalizing the Classic Greedy and Necklace Constructions of de Bruijn Sequences and Universal Cycles"],"prefix":"10.37236","volume":"23","author":[{"given":"Joe","family":"Sawada","sequence":"first","affiliation":[]},{"given":"Aaron","family":"Williams","sequence":"additional","affiliation":[]},{"given":"Dennis","family":"Wong","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2016,2,5]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i1p24\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i1p24\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T05:36:21Z","timestamp":1579239381000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v23i1p24"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,2,5]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2016,1,11]]}},"URL":"https:\/\/doi.org\/10.37236\/5517","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,2,5]]},"article-number":"P1.24"}}