Computation of Critical Exponent in Balanced Sequences

Abstract

We study balanced sequences over a d-letter alphabet. Each such sequence \(\mathbf{v}\) is described by a Sturmian sequence and two constant gap sequences \(\mathbf{y}\) and \(\mathbf{y}'\). We provide an algorithm which for a given \(\mathbf{y}\), \(\mathbf{y}'\) and a quadratic slope of a Sturmian sequence computes the critical exponent of the balanced sequence \(\mathbf{v}\).