2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66618We 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.17 pages, 2 figuresCombinatoricsMathematical Physics68R15; 05A15text