On Shift Radix Systems over Imaginary Quadratic Euclidean Domains | Zendy

Attila Pethö | Zendy; Péter Varga | Zendy; Mario Weitzer | Zendy

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On Shift Radix Systems over Imaginary Quadratic Euclidean Domains

Author(s) -

Attila Pethö,

Péter Varga,

Mario Weitzer

Publication year - 2015

Publication title -

acta cybernetica

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.143

H-Index - 18

eISSN - 2676-993X

pISSN - 0324-721X

DOI - 10.14232/actacyb.22.2.2015.14

Subject(s) - euclidean geometry , mathematics , hermitian matrix , euclidean distance matrix , quadratic equation , euclidean domain , pure mathematics , lattice (music) , integer (computer science) , euclidean distance , discrete mathematics , mathematical analysis , geometry , physics , computer science , acoustics , programming language

In this paper we generalize the shift radix systems to finite dimensionalHermitian vector spaces. Here the integer lattice is replaced bythe direct sum of imaginary quadratic Euclidean domains. We provein two cases that the set of one dimensional Euclidean shift radixsystems with finiteness property is contained in a circle of radius0.99 around the origin. Thus their structure is much simpler thanthe structure of analogous sets.

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