Combinatorial and Computational aspects of Tilings

Starting from the cubic polynomial p (x) = x^3 − ax^2 − bx ± 1, a, b ∈ Z whose solutions λi, satisfy λ1, λ2 ∈ C\R, λ3 ∈ R, |λ1| = |λ2| > 1, |λ3| < 1, let us consider the tiling substitutions with respect to p (x). In this talk, the case of the tiling substitution which generates not only positive tiles but also negative ones is discussed, and to handle it, the blocking method is introduced.