{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T14:29:15Z","timestamp":1776868155568,"version":"3.51.2"},"reference-count":19,"publisher":"American Mathematical Society (AMS)","issue":"274","license":[{"start":{"date-parts":[[2011,8,30]],"date-time":"2011-08-30T00:00:00Z","timestamp":1314662400000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    We prove Dejean\u2019s conjecture. Specifically, we show that Dejean\u2019s conjecture holds for the last remaining open values of\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"n\">\n                        <mml:semantics>\n                          <mml:mi>n<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">n<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    , namely\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"15 less-than-or-equal-to n less-than-or-equal-to 26\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mn>15<\/mml:mn>\n                            <mml:mo>\n                              \u2264\n                              \n                            <\/mml:mo>\n                            <mml:mi>n<\/mml:mi>\n                            <mml:mo>\n                              \u2264\n                              \n                            <\/mml:mo>\n                            <mml:mn>26<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">15 \\leq n \\leq 26<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    .\n                  <\/p>","DOI":"10.1090\/s0025-5718-2010-02407-x","type":"journal-article","created":{"date-parts":[[2010,12,29]],"date-time":"2010-12-29T14:39:12Z","timestamp":1293633552000},"page":"1063-1070","source":"Crossref","is-referenced-by-count":53,"title":["A proof of Dejean\u2019s conjecture"],"prefix":"10.1090","volume":"80","author":[{"given":"James","family":"Currie","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Narad","family":"Rampersad","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2010,8,30]]},"reference":[{"issue":"1","key":"1","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1016\/0304-3975(88)90009-6","article-title":"Uniformly growing \ud835\udc58th power-free homomorphisms","volume":"23","author":"Brandenburg, Franz-Josef","year":"1983","journal-title":"Theoret. Comput. Sci.","ISSN":"https:\/\/id.crossref.org\/issn\/0304-3975","issn-type":"print"},{"issue":"134","key":"2","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1093\/qmath\/34.2.145","article-title":"Nonrepetitive sequences on three symbols","volume":"34","author":"Brinkhuis, Jan","year":"1983","journal-title":"Quart. J. Math. Oxford Ser. (2)","ISSN":"https:\/\/id.crossref.org\/issn\/0033-5606","issn-type":"print"},{"issue":"1-3","key":"3","doi-asserted-by":"publisher","first-page":"137","DOI":"10.1016\/j.tcs.2007.06.001","article-title":"On Dejean\u2019s conjecture over large alphabets","volume":"385","author":"Carpi, Arturo","year":"2007","journal-title":"Theoret. Comput. Sci.","ISSN":"https:\/\/id.crossref.org\/issn\/0304-3975","issn-type":"print"},{"issue":"30-32","key":"4","doi-asserted-by":"publisher","first-page":"2885","DOI":"10.1016\/j.tcs.2009.01.026","article-title":"Dejean\u2019s conjecture holds for \ud835\udc5b\u226530","volume":"410","author":"Currie, James","year":"2009","journal-title":"Theoret. Comput. Sci.","ISSN":"https:\/\/id.crossref.org\/issn\/0304-3975","issn-type":"print"},{"key":"5","doi-asserted-by":"crossref","unstructured":"J. D. Currie, N. Rampersad, Dejean\u2019s conjecture holds for \ud835\udc5b\u226527, Theor. Inform. Appl. 43 (2009) 775\u2013778.","DOI":"10.1051\/ita\/2009017"},{"key":"6","doi-asserted-by":"publisher","first-page":"90","DOI":"10.1016\/0097-3165(72)90011-8","article-title":"Sur un th\u00e9or\u00e8me de Thue","volume":"13","author":"Dejean, Fran\u00e7oise","year":"1972","journal-title":"J. Combinatorial Theory Ser. A","ISSN":"https:\/\/id.crossref.org\/issn\/0097-3165","issn-type":"print"},{"issue":"2-3","key":"7","doi-asserted-by":"publisher","first-page":"359","DOI":"10.1016\/j.tcs.2005.07.016","article-title":"A generalization of repetition threshold","volume":"345","author":"Ilie, Lucian","year":"2005","journal-title":"Theoret. Comput. Sci.","ISSN":"https:\/\/id.crossref.org\/issn\/0304-3975","issn-type":"print"},{"issue":"1-2","key":"8","doi-asserted-by":"publisher","first-page":"70","DOI":"10.1016\/j.tcs.2007.01.020","article-title":"On critical exponents in fixed points of non-erasing morphisms","volume":"376","author":"Krieger, Dalia","year":"2007","journal-title":"Theoret. Comput. Sci.","ISSN":"https:\/\/id.crossref.org\/issn\/0304-3975","issn-type":"print"},{"key":"9","series-title":"Encyclopedia of Mathematics and its Applications","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781107326019","volume-title":"Algebraic combinatorics on words","volume":"90","author":"Lothaire, M.","year":"2002","ISBN":"https:\/\/id.crossref.org\/isbn\/0521812208"},{"key":"10","series-title":"Encyclopedia of Mathematics and its Applications","isbn-type":"print","volume-title":"Combinatorics on words","volume":"17","author":"Lothaire, M.","year":"1983","ISBN":"https:\/\/id.crossref.org\/isbn\/0201135167"},{"issue":"3","key":"11","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1051\/ita\/1992260301991","article-title":"Repetitions in the Fibonacci infinite word","volume":"26","author":"Mignosi, F.","year":"1992","journal-title":"RAIRO Inform. Th\\'{e}or. Appl.","ISSN":"https:\/\/id.crossref.org\/issn\/0988-3754","issn-type":"print"},{"issue":"3","key":"12","doi-asserted-by":"publisher","first-page":"876","DOI":"10.1016\/j.ejc.2005.11.005","article-title":"Dejean\u2019s conjecture and Sturmian words","volume":"28","author":"Mohammad-Noori, M.","year":"2007","journal-title":"European J. Combin.","ISSN":"https:\/\/id.crossref.org\/issn\/0195-6698","issn-type":"print"},{"issue":"2","key":"13","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1016\/0304-3975(92)90264-G","article-title":"Proof of Dejean\u2019s conjecture for alphabets with 5,6,7,8,9,10 and 11 letters","volume":"95","author":"Moulin Ollagnier, Jean","year":"1992","journal-title":"Theoret. Comput. Sci.","ISSN":"https:\/\/id.crossref.org\/issn\/0304-3975","issn-type":"print"},{"issue":"3","key":"14","doi-asserted-by":"publisher","first-page":"297","DOI":"10.1016\/0166-218X(84)90006-4","article-title":"\u00c0 propos d\u2019une conjecture de F. Dejean sur les r\u00e9p\u00e9titions dans les mots","volume":"7","author":"Pansiot, Jean-Jacques","year":"1984","journal-title":"Discrete Appl. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0166-218X","issn-type":"print"},{"key":"15","unstructured":"M. Rao, Last cases of Dejean\u2019s conjecture, Proc. WORDS 2009, Salerno (Italy), September 14\u201318, 2009."},{"key":"16","series-title":"Graduate Texts in Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4176-8","volume-title":"An introduction to the theory of groups","volume":"148","author":"Rotman, Joseph J.","year":"1995","ISBN":"https:\/\/id.crossref.org\/isbn\/0387942858","edition":"4"},{"key":"17","unstructured":"A. M. Shur, I. A. Gorbunova, On the growth rates of complexity of threshold languages. In the local proceedings of the 12th Mons Theoretical Computer Science Days, 2008."},{"key":"18","unstructured":"A. Thue, \u00dcber unendliche Zeichenreihen, Norske Vid. Selsk. Skr. I. Mat. Nat. Kl. Christiana 7 (1906) 1\u201322."},{"key":"19","unstructured":"A. Thue, \u00dcber die gegenseitige Lage gleicher Teile gewisser Zeichenreihen, Norske Vid. Selsk. Skr. I. Mat. Nat. Kl. Christiana 1 (1912) 1\u201367."}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2011-80-274\/S0025-5718-2010-02407-X\/S0025-5718-2010-02407-X.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2011-80-274\/S0025-5718-2010-02407-X\/S0025-5718-2010-02407-X.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T16:47:50Z","timestamp":1776790070000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2011-80-274\/S0025-5718-2010-02407-X\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,8,30]]},"references-count":19,"journal-issue":{"issue":"274","published-print":{"date-parts":[[2011,4]]}},"alternative-id":["S0025-5718-2010-02407-X"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-2010-02407-x","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[2010,8,30]]}}}