Geodesic
On the entropy and letter frequencies of ternary square-free words
The electronic journal of combinatorics, Tome 11 (2004) no. 1
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We enumerate ternary length-$\ell$ square-free words, which are words avoiding squares of all words up to length $\ell$, for $\ell\le 24$. 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.
DOI : 10.37236/1767
Classification : 68R15, 05A15 
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     author = {Christoph Richard and Uwe Grimm},
     title = {On the entropy and letter frequencies of ternary square-free words},
     journal = {The electronic journal of combinatorics},
     year = {2004},
     volume = {11},
     number = {1},
     doi = {10.37236/1767},
     zbl = {1104.68090},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1767/}
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Christoph Richard; Uwe Grimm. On the entropy and letter frequencies of ternary square-free words. The electronic journal of combinatorics, Tome 11 (2004) no. 1. doi: 10.37236/1767

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