Accessibility navigation


Generalised golden ratios over integer alphabets

Baker, S. (2014) Generalised golden ratios over integer alphabets. Integers, 14. A15. ISSN 1553-1732

[img]
Preview
Text - Accepted Version
· Please see our End User Agreement before downloading.

311kB

It is advisable to refer to the publisher's version if you intend to cite from this work. See Guidance on citing.

Abstract/Summary

It is a well known result that for β ∈ (1,1+√52) and x ∈ (0,1β−1) there exists uncountably many (ǫi)∞i=1 ∈ {0,1}N such that x = P∞i=1ǫiβ−i. When β ∈ (1+√52,2] there exists x ∈ (0,1β−1) for which there exists a unique (ǫi)∞i=1 ∈ {0,1}N such that x=P∞i=1ǫiβ−i. In this paper we consider the more general case when our sequences are elements of {0, . . . , m}N. We show that an analogue of the golden ratio exists and give an explicit formula for it.

Item Type:Article
Refereed:Yes
Divisions:Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:46858
Uncontrolled Keywords:Beta-expansions, Dimension theory
Publisher:De Gryuter

Downloads

Downloads per month over past year

University Staff: Request a correction | Centaur Editors: Update this record

Page navigation