{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T16:33:56Z","timestamp":1774370036677,"version":"3.50.1"},"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>We enumerate ternary length-$\\ell$ square-free words, which are words avoiding squares of all words up to length $\\ell$, for $\\ell\\le 24$. We analyse the singular behaviour of the corresponding generating functions. This leads to new upper entropy bounds for ternary square-free words.  We then consider ternary square-free words with fixed letter densities, thereby proving exponential growth for certain ensembles with various letter densities.  We derive consequences for the free energy and entropy of ternary square-free words.<\/jats:p>","DOI":"10.37236\/1767","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T05:23:25Z","timestamp":1578720205000},"source":"Crossref","is-referenced-by-count":12,"title":["On the Entropy and Letter Frequencies of Ternary Square-Free Words"],"prefix":"10.37236","volume":"11","author":[{"given":"Christoph","family":"Richard","sequence":"first","affiliation":[]},{"given":"Uwe","family":"Grimm","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2004,2,14]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v11i1r14\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v11i1r14\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T05:04:44Z","timestamp":1579323884000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v11i1r14"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,2,14]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2004,1,2]]}},"URL":"https:\/\/doi.org\/10.37236\/1767","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,2,14]]},"article-number":"R14"}}