On the number of Dejean words over alphabets of 5, 6, 7, 8, 9 and 10 letters

Authors:
Roman Kolpakov;Michaël Rao
Affiliations:
Moscow State University, Leninskie Gory, 119992 Moscow, Russia;LaBRI, Université Bordeaux 1, 351 cours de la libération, 33405 Talence, France
Venue:
Theoretical Computer Science
Year:
2011

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Abstract

We give lower bounds on the growth rate of Dejean words, i.e. minimally repetitive words, over a k-letter alphabet, for 5@?k@?10. Put together with the known upper bounds, we estimate these growth rates with the precision of 0.005. As a consequence, we establish the exponential growth of the number of Dejean words over a k-letter alphabet, for 5@?k@?10.