Julien Bernat - Computation of L_⊕ for several cubic Pisot numbers

dmtcs:405 - Discrete Mathematics & Theoretical Computer Science, January 1, 2007, Vol. 9 no. 2 - https://doi.org/10.46298/dmtcs.405
Computation of L_⊕ for several cubic Pisot numbers

Authors: Julien Bernat

    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.


    Volume: Vol. 9 no. 2
    Published on: January 1, 2007
    Imported on: March 26, 2015
    Keywords: [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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