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.
"Balanced words." Bull. Belg. Math. Soc. Simon Stevin 10 (5) 787 - 805, December 2003. https://doi.org/10.36045/bbms/1074791332