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On the Entropy and Letter Frequencies of Ternary Square-Free Words

Christoph Richard·Uwe Grimm
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Abstract

We enumerate all ternary length-l square-free words, which are words avoiding squares of words up to length l, for l<=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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Christoph Richard, Uwe Grimm. 2003-03-19. On the Entropy and Letter Frequencies of Ternary Square-Free Words. https://arxiv.org/abs/math/0302302

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