Balanced pair algorithm for a class of cubic substitutions

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 geq b geq 1. Applying the balanced pair algorithm to these substitutions, we obtain a general formula for the associated intersection substitution.