{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:08Z","timestamp":1753893848036,"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>We identify the structure of the lexicographically least word avoiding $5\/4$-powers on the alphabet of nonnegative integers. Specifically, we show that this word has the form $\\mathbf{p} \\, \\tau ( \\varphi(\\mathbf{z}) \\varphi^2(\\mathbf{z}) \\cdots)$ where $\\mathbf{p},\\mathbf{z}$ are finite words, $\\varphi$ is a $6$-uniform morphism, and $\\tau$ is a coding. This description yields a recurrence for the $i$th letter, which we use to prove that the sequence of letters is $6$-regular with rank $188$. More generally, we prove $k$-regularity for a sequence satisfying a recurrence of the same type.<\/jats:p>","DOI":"10.37236\/9581","type":"journal-article","created":{"date-parts":[[2020,9,4]],"date-time":"2020-09-04T02:47:29Z","timestamp":1599187649000},"source":"Crossref","is-referenced-by-count":0,"title":["Avoiding 5\/4-Powers on the Alphabet of Nonnegative Integers"],"prefix":"10.37236","volume":"27","author":[{"given":"Eric","family":"Rowland","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Manon","family":"Stipulanti","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2020,8,21]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i3p42\/8160","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i3p42\/8160","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,9,4]],"date-time":"2020-09-04T02:47:29Z","timestamp":1599187649000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v27i3p42"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,8,21]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2020,7,9]]}},"URL":"https:\/\/doi.org\/10.37236\/9581","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2020,8,21]]},"article-number":"P3.42"}}