Balanced pair algorithm for a class of cubic substitutions

Abstract

In this article we introduce the balanced pair algorithm associated with 2 unimodular Pisot substitutions having the same incidence matrix. We are interested in beta-substitution related to the polynomial x 3 − ax 2 − bx − 1 for a ≥ b ≥ 1 . Applying the balanced pair algorithm to these substitutions, we obtain a general formula for the associated intersection substitution.