{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T11:55:59Z","timestamp":1776858959439,"version":"3.51.2"},"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 2017, Vesti proposed the problem of determining the repetition threshold for infinite rich words, i.e., for infinite words in which all factors of length $n$ contain $n$ distinct nonempty palindromic factors. In 2020, Currie, Mol, and Rampersad proved a conjecture of Baranwal and Shallit that the repetition threshold for binary rich words is $2 + \\sqrt{2}\/2$. In this paper, we prove a structure theorem for $16\/7$-power-free ternary rich words. Using the structure theorem, we deduce that the repetition threshold for ternary rich words is $1 + 1\/(3 - \\mu) \\approx 2.25876324$, where $\\mu$ is the unique real root of the polynomial $x^3 - 2x^2 - 1$.<\/jats:p>","DOI":"10.37236\/13499","type":"journal-article","created":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T15:19:02Z","timestamp":1750346342000},"source":"Crossref","is-referenced-by-count":1,"title":["The Repetition Threshold for Ternary Rich Words"],"prefix":"10.37236","volume":"32","author":[{"given":"James","family":"Currie","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lucas","family":"Mol","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jarkko","family":"Peltom\u00e4ki","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2025,6,20]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v32i2p55\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v32i2p55\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T15:19:02Z","timestamp":1750346342000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v32i2p55"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,6,20]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2025,4,11]]}},"URL":"https:\/\/doi.org\/10.37236\/13499","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,6,20]]},"article-number":"P2.55"}}