Computation of L⊕ for several cubic Pisot numbers
Julien Bernat
Abstract
In this article, we are dealing with β-numeration,
which is a generalization of numeration in a non-integer base. We
consider the class of simple Parry numbers such that
dβ(1) = 0.k1d-1 kd
with d ∈ ℕ, d ≥ 2 and
k1 ≥ kd ≥ 1. We prove that
these elements define Rauzy fractals that are stable under a central
symmetry. We use this result to compute, for several cases of cubic
Pisot units, the maximal length among the lengths of the finite
β-fractional parts of sums of two
β-integers, denoted by
L⊕. In particular, we prove that
L⊕ = 5 in the Tribonacci case.
Full Text: PostScript PDF