FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2007, VOLUME 13, NUMBER 5, PAGES 213-224

Balanced words and dynamical systems

A. L. Chernyatiev

Abstract

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This article is devoted to the description of all nonperiodic balanced words with $n$ different letters. A superword $W$ is called balanced if the numbers of equal letters in any two of its factors (subwords) $u$₁ and $u$₂ of equal length differ by at most $1$. Balanced words are one of the possible generalizations of Sturmian words. We give a geometric interpretation of nonperiodic balanced sequences over an $n$-letter alphabet.

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Last modified: February 18, 2008