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Asymptotic Behavior of Beta-Integers
Balková L., Gazeau J.-P., Pelantová E.
Letters in Mathematical Physics 84 (2008) 179-198 - http://hal.in2p3.fr/in2p3-00326547
Mathématiques/Physique mathématique
Asymptotic Behavior of Beta-Integers
L. Balková1, J.-P. Gazeau1, E. Pelantová
1 :  APC - UMR 7164 - AstroParticule et Cosmologie
CNRS : UMR7164 – IN2P3 – Observatoire de Paris – Université Paris VII - Paris Diderot – CEA : DSM/IRFU
APC - UMR 7164, Université Paris Diderot, 10 rue Alice Domon et Léonie Duquet, case postale 7020, F-75205 Paris Cedex 13
Beta-integers ("β-integers") are those numbers which are the counterparts of integers when real numbers are expressed in an irrational base β > 1. In quasicrystalline studies, β-integers supersede the "crystallographic" ordinary integers. When the number β is a Parry number, the corresponding β-integers realize only a finite number of distances between consecutive elements and are in this sense the most comparable to ordinary integers. In this paper, we point out the similarity of β-integers and ordinary integers in the asymptotic sense, in particular for a subclass of Parry numbers - Pisot numbers for which their Parry and minimal polynomial coincide.

Articles dans des revues avec comité de lecture
Letters in Mathematical Physics (Lett. Math. Phys.)
Publisher Springer Verlag (Germany)
ISSN 0377-9017 (eISSN : 1573-0530)

beta-integers – beta-numeration – asymptotic behavior – quasicrystals – aperiodic structure
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