On the symmetric intersection of Rauzy fractals associated with the k-bonacci substitution

Abstract

In this article, we study the intersection of Rauzy fractals associated with the k-bonacci substitution and its reversed substitution. Applying balanced pair algorithm to these two substitutions, we characterise all minimal balanced pairs, and we obtain a general formula for the associated intersection substitution. This substitution is defined over k(k+1) 2 letters.