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Computation of L_⊕ for several cubic Pisot numbers

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.
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Julien Bernat. Computation of L_⊕ for several cubic Pisot numbers. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2007, Vol. 9 no. 2 (2), pp.175--193. ⟨10.46298/dmtcs.405⟩. ⟨hal-00966525⟩



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