{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,5]],"date-time":"2025-10-05T04:38:07Z","timestamp":1759639087589,"version":"3.41.2"},"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>A word is square-free if it does not contain nonempty factors of the form $XX$. In 1906 Thue proved that there exist arbitrarily long square-free words over a $3$-letter alphabet. We consider a new type of square-free words with additional property. A square-free word is called extremal\u00a0if it cannot be extended to a new square-free word by inserting a single letter at any position. We prove that there exist infinitely many square-free extremal words over a $3$-letter alphabet. Some parts of our construction relies on computer verifications. It is not known if there exist any extremal square-free words over a $4$-letter alphabet.<\/jats:p>","DOI":"10.37236\/9264","type":"journal-article","created":{"date-parts":[[2020,3,19]],"date-time":"2020-03-19T00:37:25Z","timestamp":1584578245000},"source":"Crossref","is-referenced-by-count":0,"title":["Extremal Square-Free Words"],"prefix":"10.37236","volume":"27","author":[{"given":"Jaros\u0142aw","family":"Grytczuk","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hubert","family":"Kordulewski","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Artur","family":"Niewiadomski","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2020,3,6]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i1p48\/8036","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i1p48\/8036","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,3,19]],"date-time":"2020-03-19T00:37:25Z","timestamp":1584578245000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v27i1p48"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,3,6]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2020,1,9]]}},"URL":"https:\/\/doi.org\/10.37236\/9264","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2020,3,6]]},"article-number":"P1.48"}}