The entropy of square-free words

Authors:
M. Baake;V. Elser;U. Grimm
Affiliations:
Institut für Theoretische Physik, Universität Tübingen Auf der Morgenstelle 14, 72076 Tübingen, Germany;Institut für Theoretische Physik, Universität Tübingen Auf der Morgenstelle 14, 72076 Tübingen, Germany and Laboratory of Atomic and Solid State Physics Cornell University, Ith ...;Instituut voor Theoretische Fysica, Universiteit van Amsterdam Valckenierstraat 65, 1018 XE Amsterdam, The Netherlands
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
1997

Citing 3
Cited 3

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Abstract

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.