منابع مشابه
Beta-integers as a Group
Discrete sets of numbers related to some irrational number , called the-integers Z , are a natural tool to describe quasicrystals. We prove that, when is a quadratic Pisot unit, the set Z is a group isomorphic to the set of integers Z.
متن کاملVoronoi Cells of Beta-Integers
In this paper are considered one-dimensional tilings arising from some Pisot numbers encountered in quasicrystallography as the quadratic Pisot units and the cubic Pisot unit associated with 7-fold symmetry, and also the Tribonacci number. We give characterizations of the Voronoi cells of such tilings, using word combinatorics and substitutions.
متن کاملSubstitutions over infinite alphabet generating (-\beta)-integers
This contribution is devoted to the study of positional numeration systems with negative base introduced by Ito and Sadahiro in 2009, called (−β )-expansions. We give an admissibility criterion for more general case of (−β )-expansions and discuss the properties of the set of (−β )-integers, denoted by Z−β . We give a description of distances within Z−β and show that this set can be coded by an...
متن کاملOn the Delone property of (-\beta)-integers
These sets were introduced in the domain of quasicrystallography, see e.g. [2]. It is not difficult to see that Z−β =Z when β ∈Z, and that Z−β = {0} when β < 1+ √ 5 2 . For β ≥ 1+ √ 5 2 , Ambrož et al. [1] showed that Z−β can be described by the fixed point of an anti-morphism on a possibly infinite alphabet. They also calculated explicitely the set of distances between consecutive (−β )-intege...
متن کاملBeta - Integers as Natural Counting Systems
Recently, discrete sets of numbers, the-integers ZZ , have been proposed as numbering tools in quasicrystalline studies. Indeed, there exists a unique numeration system based on the irrational > 1 in which the-integers are all real numbers with no fractional part. These-integers appear as being quite appropriate to describing some quasilattices relevant to quasicrystallography when precisely is...
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ژورنال
عنوان ژورنال: Letters in Mathematical Physics
سال: 2009
ISSN: 0377-9017,1573-0530
DOI: 10.1007/s11005-009-0301-z