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
Session Chair
Naim Preniqi
Session Co-Chair
Blerton Abazi
Proceedings Editor
Edmond Hajrizi
ISBN
978-9951-437-54-7
Location
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
Recommended Citation
Baushi, Arben; Zaka, Orgest; and Xhoxhi, Olsi, "Same Property of Beta-expansion" (2017). UBT International Conference. 197.
https://knowledgecenter.ubt-uni.net/conference/2017/all-events/197
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.