### Abstract

In this paper we generalize the shift radix systems to finite dimensional Hermitian vector spaces. Here the integer lattice is replaced by the direct sum of imaginary quadratic Euclidean domains. We prove in two cases that the set of one dimensional Euclidean shift radix systems with finiteness property is contained in a circle of radius 0.99 around the origin. Thus their structure is much simpler than the structure of analogous sets.

Original language | English |
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Pages (from-to) | 485-498 |

Number of pages | 14 |

Journal | Acta Cybernetica |

Volume | 22 |

Issue number | 2 |

Publication status | Published - 2015 |

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### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Theoretical Computer Science

### Cite this

*Acta Cybernetica*,

*22*(2), 485-498.

**On shift radix systems over imaginary quadratic Euclidean domains.** / Pethő, A.; Varga, Peter; Weitzer, Mario.

Research output: Contribution to journal › Article

*Acta Cybernetica*, vol. 22, no. 2, pp. 485-498.

}

TY - JOUR

T1 - On shift radix systems over imaginary quadratic Euclidean domains

AU - Pethő, A.

AU - Varga, Peter

AU - Weitzer, Mario

PY - 2015

Y1 - 2015

N2 - In this paper we generalize the shift radix systems to finite dimensional Hermitian vector spaces. Here the integer lattice is replaced by the direct sum of imaginary quadratic Euclidean domains. We prove in two cases that the set of one dimensional Euclidean shift radix systems with finiteness property is contained in a circle of radius 0.99 around the origin. Thus their structure is much simpler than the structure of analogous sets.

AB - In this paper we generalize the shift radix systems to finite dimensional Hermitian vector spaces. Here the integer lattice is replaced by the direct sum of imaginary quadratic Euclidean domains. We prove in two cases that the set of one dimensional Euclidean shift radix systems with finiteness property is contained in a circle of radius 0.99 around the origin. Thus their structure is much simpler than the structure of analogous sets.

UR - http://www.scopus.com/inward/record.url?scp=84955499107&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84955499107&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84955499107

VL - 22

SP - 485

EP - 498

JO - Acta Cybernetica

JF - Acta Cybernetica

SN - 0324-721X

IS - 2

ER -