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On the Entropy and Letter Frequencies of Ternary SquareFree Words
, 2003
"... We enumerate all ternary lengthℓ squarefree 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 squarefree words. We then consider ternary squar ..."
Abstract

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We enumerate all ternary lengthℓ squarefree 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 squarefree words. We then consider ternary squarefree 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 squarefree words.