On the entropy and letter frequencies of ternary square-free words

Richard, Christoph and Grimm, Uwe (2004). On the entropy and letter frequencies of ternary square-free words. Electronic Journal of Combinatorics, 11(1) R14.

Abstract

We enumerate all ternary length-1 square-free words, which are words avoiding squares of words up to length 1, for 1<=24. We analyse the singular behaviour of the corresponding generating functions. This leads to new upper entropy bounds for ternary square-free words. We then consider ternary square-free words with
fixed letter densities, thereby proving exponential growth for certain ensembles with various letter densities. We derive consequences for the free energy and entropy of
ternary square-free words.

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