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

Abstract

We give lower bounds on the growth rate of Dejean words, i.e. minimally repetitive words, over a k-letter alphabet, for k=5, 6, 7, 8, 9, 10. Put together with the known upper bounds, we estimate these growth rates with the precision of 0,005. As an consequence, we establish the exponential growth of the number of Dejean words over a k-letter alphabet, for k=5, 6, 7, 8, 9, 10.