{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:45Z","timestamp":1753893825755,"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>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 $x$ of $w$ and no non-erasing morphism $h$ from $\\Delta^*$ to $\\Sigma^*$ such that $h(p) = x$.  Bell and Goh have recently applied an algebraic technique due to Golod to show that for a certain wide class of patterns $p$ there are exponentially many words of length $n$ over a $4$-letter alphabet that avoid $p$.  We consider some further consequences of their work.  In particular, we show that any pattern with $k$ variables of length at least $4^k$ is avoidable on the binary alphabet.  This improves an earlier bound due to Cassaigne and Roth.<\/jats:p>","DOI":"10.37236\/621","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:46:31Z","timestamp":1578714391000},"source":"Crossref","is-referenced-by-count":6,"title":["Further Applications of a Power Series Method for Pattern Avoidance"],"prefix":"10.37236","volume":"18","author":[{"given":"Narad","family":"Rampersad","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2011,6,21]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p134\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p134\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:08:42Z","timestamp":1579302522000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v18i1p134"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,6,21]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2011,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/621","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2011,6,21]]},"article-number":"P134"}}