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December 2003 Balanced words
Laurent Vuillon
Bull. Belg. Math. Soc. Simon Stevin 10(5): 787-805 (December 2003). DOI: 10.36045/bbms/1074791332


This article presents a survey about balanced words. The balance property comes from combinatorics on words and is used as a characteristic property of the well-known Sturmian words. The main goal of this survey is to study various generalizations of this notion with applications and with open problems in number theory and in theoretical computer science. We also prove a new result about the generalized balance property of hypercubic billiard words.


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Laurent Vuillon. "Balanced words." Bull. Belg. Math. Soc. Simon Stevin 10 (5) 787 - 805, December 2003.


Published: December 2003
First available in Project Euclid: 22 January 2004

zbMATH: 1070.68129
MathSciNet: MR2073026
Digital Object Identifier: 10.36045/bbms/1074791332

Keywords: Arnoux-Rauzy words , Balanced words , Beatty sequences , combinatorics on words , complexity function , heap of pieces , hypercubic billiard words , optimization problems , Sturmian words

Rights: Copyright © 2003 The Belgian Mathematical Society


Vol.10 • No. 5 • December 2003
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