2008/02/21 by Ľubomíra Balková, L. Balková, Jean‐Pierre Gazeau +3
Computer Science · Materials Science · Mathematics · Physics and Astronomy · #Algebraic number #Combinatorics #Discrete mathematics #Eisenstein integer #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematics #Quadratic integer #Quasicrystal Structures and Properties #Sequence (biology) #math-ph #math.MP #semigroups and automata theory
paper · pdf · doi:10.1007/s11005-008-0241-z
17 pages
arxiv created 2008/02/21 · openalex publication_date 2008/05/21 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Beta-integers (``β-integers'') are those numbers which are the counterparts of integers when real numbers are expressed in irrational basis 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 somewhat appear like ordinary integers, mainly in an asymptotic sense. In this letter we make precise this asymptotic behavior by proving four theorems concerning Parry β-integers.