The Entropy of Square-Free Words
classification
🧮 math-ph
math.COmath.MP
keywords
entropyletterssquare-freewordsalphabetsapproximateasymptoticallybounds
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Finite alphabets of at least three letters permit the construction of square-free words of infinite length. We show that the entropy density is strictly positive and derive reasonable lower and upper bounds. Finally, we present an approximate formula which is asymptotically exact with rapid convergence in the number of letters.
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