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 the 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 dened over k(k+1) letters.

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Key words: Substitutions, k-bonacci, balanced pairs algorithm, fractal sets.