Extremal properties of (epi)Sturmian sequences and distribution modulo 1

Allouche, J-P. and Glen, A. (2010) Extremal properties of (epi)Sturmian sequences and distribution modulo 1. L’Enseignement Mathématique, 56 . pp. 365-401.

Abstract

Starting from a study of Y. Bugeaud and A. Dubickas (2005) on a question in distribution of real numbers modulo 1 via combinatorics on words, we survey some combinatorial properties of (epi)Sturmian sequences and distribution modulo 1 in connection to their work. In particular we focus on extremal properties of (epi)Sturmian sequences, some of which have been rediscovered several times.