Geodesic
Computation of L_⊕ for several cubic Pisot numbers
Discrete mathematics & theoretical computer science, Tome 9 (2007) no. 2.

Voir la notice de l'article provenant de la source Episciences

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. 
@article{DMTCS_2007_9_2_a10,
     author = {Bernat, Julien},
     title = {Computation of {L_\ensuremath{\oplus}} for several cubic {Pisot} numbers},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {9},
     number = {2},
     year = {2007},
     doi = {10.46298/dmtcs.405},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.405/}
}
TY  - JOUR
AU  - Bernat, Julien
TI  - Computation of L_⊕ for several cubic Pisot numbers
JO  - Discrete mathematics & theoretical computer science
PY  - 2007
VL  - 9
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.405/
DO  - 10.46298/dmtcs.405
LA  - en
ID  - DMTCS_2007_9_2_a10
ER  - 
%0 Journal Article
%A Bernat, Julien
%T Computation of L_⊕ for several cubic Pisot numbers
%J Discrete mathematics & theoretical computer science
%D 2007
%V 9
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.405/
%R 10.46298/dmtcs.405
%G en
%F DMTCS_2007_9_2_a10
Bernat, Julien. Computation of L_⊕ for several cubic Pisot numbers. Discrete mathematics & theoretical computer science, Tome 9 (2007) no. 2. doi : 10.46298/dmtcs.405. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.405/

Cité par Sources :