{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T16:16:06Z","timestamp":1759335366276,"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 1906 Axel Thue showed how to construct an infinite non-repetitive (or square-free) word on an alphabet of size 3.  Since then this result has been rediscovered many times and extended in many ways.  We present a two-dimensional version of this result.  We show how to construct a rectangular tiling of the plane using 5 symbols which has the property that lines of tiles which are horizontal, vertical or have slope +1 or $-1$ contain no repetitions.  As part of the construction we introduce a new type of word, one that is non-repetitive up to mod k, which is of interest in itself.  We also indicate how our results might be extended to higher dimensions.<\/jats:p>","DOI":"10.37236\/1644","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:25:40Z","timestamp":1578709540000},"source":"Crossref","is-referenced-by-count":8,"title":["Non-Repetitive Tilings"],"prefix":"10.37236","volume":"9","author":[{"given":"James D.","family":"Currie","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jamie","family":"Simpson","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2002,7,3]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v9i1r28\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v9i1r28\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T05:13:50Z","timestamp":1579324430000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v9i1r28"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,7,3]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2002,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1644","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2002,7,3]]},"article-number":"R28"}}