Arithmetics in numeration systems with negative quadratic base

Title:

Arithmetics in numeration systems with negative quadratic base

Creator:

Masáková, Zuzana and Vávra, Tomáš

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:c6232bf8-2e43-45ec-8e76-4cae006aa38d
uuid:c6232bf8-2e43-45ec-8e76-4cae006aa38d

Subject:

numeration systems, negative base, and Pisot number

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

We consider positional numeration system with negative base −β, as introduced by Ito and Sadahiro. In particular, we focus on arithmetical properties of such systems when β is a quadratic Pisot number. We study a class of roots β>1 of polynomials x2−mx−n, m≥n≥1, and show that in this case the set Fin(−β) of finite (−β)-expansions is closed under addition, although it is not closed under subtraction. A particular example is β=τ=12(1+5–√), the golden ratio. For such β, we determine the exact bound on the number of fractional digits appearing in arithmetical operations. We also show that the set of (−τ)-integers coincides on the positive half-line with the set of (τ2)-integers.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

[74]-92

Source:

Kybernetika | 2011 Volume:47 | Number:1

Harvested from:

CDK

Metadata only:

false