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

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.

References in corpus (3)

• A devil's staircase from rotations and irrationality measures for Liouville numbers
• Directive words of episturmian words: equivalences and normalization
• A local balance property of episturmian words

Cited by in corpus (1)

• Periodicity, repetitions, and orbits of an automatic sequence