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

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

2011-05-16

arxiv.org/abs/1105.3116v1

Computer Science

Formal Languages and Automata Theory

13 pages

Scientific paper

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.

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