## All Events

#### Event Title

Same Property of Beta-expansion

#### Session

Information Systems and Security

#### Description

Peoples over the ages use different counting systems. Appling that to cryptography, we use to represent numbers with a small number of non-zero digits. The problem of finding representations with minimal numbers of digits has been solved for integer bases. In this paper, we consider numeration systems with respect to a real base which is a Pisot numbers. The theory of beta-expansion creat a link between symbolic dynamics and a part of number theory. On this papers we give a Pisot numers with the finiteness property (F) and with weak finiteness property (W). The set of numbers with finite greedy expansion defined by Frougny and Solomyak is exactly Z[β-1]∩[0,1]. Same examples with finetnes propety is given in the end of this work with beta –expansion of numbers 1.

#### Keywords:

Counting systems, Pisot number, Beta-expansion, Cryptography

Naim Preniqi

Blerton Abazi

Edmond Hajrizi

#### ISBN

978-9951-437-54-7

Durres, Albania

#### Start Date

28-10-2017 4:00 PM

#### End Date

28-10-2017 5:30 PM

#### DOI

10.33107/ubt-ic.2017.197

#### Share

COinS

Oct 28th, 4:00 PM Oct 28th, 5:30 PM

Same Property of Beta-expansion

Durres, Albania

Peoples over the ages use different counting systems. Appling that to cryptography, we use to represent numbers with a small number of non-zero digits. The problem of finding representations with minimal numbers of digits has been solved for integer bases. In this paper, we consider numeration systems with respect to a real base which is a Pisot numbers. The theory of beta-expansion creat a link between symbolic dynamics and a part of number theory. On this papers we give a Pisot numers with the finiteness property (F) and with weak finiteness property (W). The set of numbers with finite greedy expansion defined by Frougny and Solomyak is exactly Z[β-1]∩[0,1]. Same examples with finetnes propety is given in the end of this work with beta –expansion of numbers 1.