Beta-integers as a Group
نویسنده
چکیده
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.
منابع مشابه
Examples of non-quasicommutative semigroups decomposed into unions of groups
Decomposability of an algebraic structure into the union of its sub-structures goes back to G. Scorza's Theorem of 1926 for groups. An analogue of this theorem for rings has been recently studied by A. Lucchini in 2012. On the study of this problem for non-group semigroups, the first attempt is due to Clifford's work of 1961 for the regular semigroups. Since then, N.P. Mukherjee in 1972 studied...
متن کاملSymmetry groups for beta-lattices
We present a construction of symmetry plane-groups for quasiperiodic point-sets in the plane, named beta-lattices. The algebraic framework is issued from counting systems called beta-integers, determined by Pisot-Vijayaraghavan (PV) algebraic integers β > 1. The beta-integer sets can be equipped with abelian group structures and internal multiplicative laws. These arithmetic structures lead to ...
متن کامل$Z_k$-Magic Labeling of Some Families of Graphs
For any non-trivial abelian group A under addition a graph $G$ is said to be $A$-textit{magic} if there exists a labeling $f:E(G) rightarrow A-{0}$ such that, the vertex labeling $f^+$ defined as $f^+(v) = sum f(uv)$ taken over all edges $uv$ incident at $v$ is a constant. An $A$-textit{magic} graph $G$ is said to be $Z_k$-magic graph if the group $A$ is $Z_k$ the group of integers modulo $k...
متن کاملOn a sequence related to the coprime integers
The asymptotic behaviour of the sequence with general term $P_n=(varphi(1)+varphi(2)+cdots+varphi(n))/(1+2+cdots+n)$, is studied which appears in the studying of coprime integers, and an explicit bound for the difference $P_n-6/pi^2$ is found.
متن کاملNon-Abelian Sequenceable Groups Involving ?-Covers
A non-abelian finite group is called sequenceable if for some positive integer , is -generated ( ) and there exist integers such that every element of is a term of the -step generalized Fibonacci sequence , , , . A remarkable application of this definition may be find on the study of random covers in the cryptography. The 2-step generalized sequences for the dihedral groups studi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1999