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Letters in Mathematical Physics 84 (2008) 179-198
Asymptotic Behavior of Beta-Integers
L. Balková1, J.-P. Gazeau1, E. Pelantová

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.
1 :  APC - UMR 7164 - AstroParticule et Cosmologie
Mathématiques/Physique mathématique
beta-integers – beta-numeration – asymptotic behavior – quasicrystals – aperiodic structure
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