{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T11:56:45Z","timestamp":1776859005180,"version":"3.51.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","issue":"Analysis of Algorithms","license":[{"start":{"date-parts":[[2020,2,24]],"date-time":"2020-02-24T00:00:00Z","timestamp":1582502400000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"},{"start":{"date-parts":[[2020,2,24]],"date-time":"2020-02-24T00:00:00Z","timestamp":1582502400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"},{"start":{"date-parts":[[2020,2,24]],"date-time":"2020-02-24T00:00:00Z","timestamp":1582502400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2025,4,1]]},"abstract":"<jats:p>A word of length $n$ is rich if it contains $n$ nonempty palindromic factors. An infinite word is rich if all of its finite factors are rich. Baranwal and Shallit produced an infinite binary rich word with critical exponent $2+\\sqrt{2}\/2$ ($\\approx 2.707$) and conjectured that this was the least possible critical exponent for infinite binary rich words (i.e., that the repetition threshold for binary rich words is $2+\\sqrt{2}\/2$). In this article, we give a structure theorem for infinite binary rich words that avoid $14\/5$-powers (i.e., repetitions with exponent at least 2.8). As a consequence, we deduce that the repetition threshold for binary rich words is $2+\\sqrt{2}\/2$, as conjectured by Baranwal and Shallit. This resolves an open problem of Vesti for the binary alphabet; the problem remains open for larger alphabets.<\/jats:p>\n                  <jats:p>Comment: 16 pages<\/jats:p>","DOI":"10.23638\/dmtcs-22-1-6","type":"journal-article","created":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T12:57:53Z","timestamp":1743685073000},"source":"Crossref","is-referenced-by-count":3,"title":["The repetition threshold for binary rich words"],"prefix":"10.23638","volume":"vol. 22 no. 1","author":[{"given":"James D.","family":"Currie","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lucas","family":"Mol","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Narad","family":"Rampersad","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2020,2,24]]},"container-title":["Discrete Mathematics &amp; Theoretical Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/1908.03169v4","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/1908.03169v4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T12:57:53Z","timestamp":1743685073000},"score":1,"resource":{"primary":{"URL":"http:\/\/dmtcs.episciences.org\/5791"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,2,24]]},"references-count":0,"journal-issue":{"issue":"Analysis of Algorithms","published-online":{"date-parts":[[2020,2,24]]}},"URL":"https:\/\/doi.org\/10.23638\/dmtcs-22-1-6","relation":{"has-preprint":[{"id-type":"arxiv","id":"1908.03169v3","asserted-by":"subject"},{"id-type":"arxiv","id":"1908.03169v2","asserted-by":"subject"}],"has-review":[{"id-type":"uri","id":"https:\/\/zbmath.org\/7268106","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"1908.03169","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1908.03169","asserted-by":"subject"}],"is-cited-by":[{"id-type":"doi","id":"10.1007\/978-3-030-68195-1_23","asserted-by":"object"}]},"ISSN":["1365-8050"],"issn-type":[{"value":"1365-8050","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,2,24]]},"article-number":"5791"}}