{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:13Z","timestamp":1753893793389,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>The lexicographically least square-free infinite word on the alphabet of non-negative integers with a given prefix $p$ is denoted $L(p)$. When $p$ is the empty word, this word was shown by Guay-Paquet and Shallit to be the ruler sequence. For other prefixes, the structure is significantly more complicated. In this paper, we show that $L(p)$ reflects the structure of the ruler sequence for several words $p$. We provide morphisms that generate $L(n)$ for letters $n=1$ and $n\\geq3$, and $L(p)$ for most families of two-letter words $p$.<\/jats:p>","DOI":"10.37236\/11659","type":"journal-article","created":{"date-parts":[[2023,7,27]],"date-time":"2023-07-27T17:14:11Z","timestamp":1690478051000},"source":"Crossref","is-referenced-by-count":0,"title":["The Lexicographically Least Square-Free Word with a Given Prefix"],"prefix":"10.37236","volume":"30","author":[{"given":"Siddharth","family":"Berera","sequence":"first","affiliation":[]},{"given":"Andr\u00e9s","family":"G\u00f3mez-Colunga","sequence":"additional","affiliation":[]},{"given":"Joey","family":"Lakerdas-Gayle","sequence":"additional","affiliation":[]},{"given":"John","family":"L\u00f3pez","sequence":"additional","affiliation":[]},{"given":"Mauditra","family":"Matin","sequence":"additional","affiliation":[]},{"given":"Daniel","family":"Roebuck","sequence":"additional","affiliation":[]},{"given":"Eric","family":"Rowland","sequence":"additional","affiliation":[]},{"given":"Noam","family":"Scully","sequence":"additional","affiliation":[]},{"given":"Juliet","family":"Whidden","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2023,7,28]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v30i3p11\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v30i3p11\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,7,27]],"date-time":"2023-07-27T17:14:23Z","timestamp":1690478063000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v30i3p11"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,7,28]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2023,7,14]]}},"URL":"https:\/\/doi.org\/10.37236\/11659","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2023,7,28]]},"article-number":"P3.11"}}