{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:56Z","timestamp":1753893836680,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>We study the lexicographically least infinite $a\/b$-power-free word on the alphabet of non-negative integers.\u00a0Frequently this word is a fixed point of a uniform morphism, or closely related to one.\u00a0For example, the lexicographically least $7\/4$-power-free word is a fixed point of a $50847$-uniform morphism.\u00a0We identify the structure of the lexicographically least $a\/b$-power-free word for three infinite families of rationals $a\/b$ as well many \"sporadic\" rationals that do not seem to belong to general families.\u00a0To accomplish this, we develop an automated procedure for proving $a\/b$-power-freeness for morphisms of a certain form, both for explicit and symbolic rational numbers $a\/b$.\u00a0Finally, we establish a connection to words on a finite alphabet.\u00a0Namely, the lexicographically least $27\/23$-power-free word is in fact a word on the finite alphabet $\\{0, 1, 2\\}$, and its sequence of letters is $353$-automatic.<\/jats:p>","DOI":"10.37236\/6678","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T15:33:23Z","timestamp":1578670403000},"source":"Crossref","is-referenced-by-count":2,"title":["Avoiding Fractional Powers over the Natural Numbers"],"prefix":"10.37236","volume":"25","author":[{"given":"Lara","family":"Pudwell","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0359-8381","authenticated-orcid":false,"given":"Eric","family":"Rowland","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2018,5,25]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i2p27\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i2p27\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:33:43Z","timestamp":1579235623000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v25i2p27"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,5,25]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2018,4,13]]}},"URL":"https:\/\/doi.org\/10.37236\/6678","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2018,5,25]]},"article-number":"P2.27"}}