Discrete Mathematics & Theoretical Computer Science,Vol 9, No 2 (2007)

摘要

In this article, we are dealing with β-numeration,which is a generalization of numeration in a non-integer base. Weconsider the class of simple Parry numbers such thatdβ(1) = 0.k1d-1 kdwith d ∈ ?, d ≥ 2 andk1 ≥ kd ≥ 1. We prove thatthese elements define Rauzy fractals that are stable under a centralsymmetry. We use this result to compute, for several cases of cubicPisot units, the maximal length among the lengths of the finiteβ-fractional parts of sums of twoβ-integers, denoted byL⊕. In particular, we prove thatL⊕ = 5 in the Tribonacci case.