{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T16:19:29Z","timestamp":1759335569267,"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>A sequence $S=s_{1}s_{2}\\ldots s_{n}$ is said to be nonrepetitive if no two adjacent blocks of $S$ are identical. In 1906 Thue proved that there exist arbitrarily long nonrepetitive sequences over $3$-element set of symbols. We study a generalization of nonrepetitive sequences involving arithmetic progressions. We prove that for every $k\\geqslant 1$, there exist arbitrarily long sequences over at most $2k+10 \\sqrt{k}$ symbols whose subsequences, indexed by arithmetic progressions with common differences from the set $\\{1,2,\\ldots ,k\\}$, are nonrepetitive. This improves a previous bound of $e^{33}k$ obtained by Grytczuk. Our approach is based on a technique introduced recently by Grytczuk Kozik and Micek, which was originally inspired by a constructive proof of the Lov\u00e1sz Local Lemma due to Moser and Tardos. We also discuss some related problems that can be  attacked by this method.<\/jats:p>","DOI":"10.37236\/696","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:40:46Z","timestamp":1578714046000},"source":"Crossref","is-referenced-by-count":5,"title":["Nonrepetitive Sequences on Arithmetic Progressions"],"prefix":"10.37236","volume":"18","author":[{"given":"Jaros\u0142aw","family":"Grytczuk","sequence":"first","affiliation":[]},{"given":"Jakub","family":"Kozik","sequence":"additional","affiliation":[]},{"given":"Marcin","family":"Witkowski","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2011,10,31]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p209\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p209\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:00:32Z","timestamp":1579302032000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v18i1p209"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,10,31]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2011,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/696","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2011,10,31]]},"article-number":"P209"}}