{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:33Z","timestamp":1753893813720,"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>In combinatorics on words, a word $w$ over an alphabet $\\Sigma$ is said to avoid a pattern $p$ over an alphabet $\\Delta$ if there is no factor $f$ of $w$ such that $f= h(p)$ where $h: \\Delta^*\\to\\Sigma^*$ is a non-erasing morphism. A pattern $p$ is said to be $k$-avoidable if there exists an infinite word over a $k$-letter alphabet that avoids $p$. We give a positive answer to Problem 3.3.2 in Lothaire's book \"Algebraic combinatorics on words'\", that is, every pattern with $k$ variables of length at least $2^k$ (resp. $3\\times2^{k-1}$) is 3-avoidable (resp. 2-avoidable). This conjecture was first stated by Cassaigne in his thesis in 1994. This improves previous bounds due to Bell and Goh, and Rampersad.<\/jats:p>","DOI":"10.37236\/3038","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T01:06:22Z","timestamp":1578704782000},"source":"Crossref","is-referenced-by-count":5,"title":["Application of Entropy Compression in Pattern Avoidance"],"prefix":"10.37236","volume":"21","author":[{"given":"Pascal","family":"Ochem","sequence":"first","affiliation":[]},{"given":"Alexandre","family":"Pinlou","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2014,4,16]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v21i2p7\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v21i2p7\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T11:01:03Z","timestamp":1579258863000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v21i2p7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,4,16]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2014,3,31]]}},"URL":"https:\/\/doi.org\/10.37236\/3038","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2014,4,16]]},"article-number":"P2.7"}}