Baur, K orcid.org/0000-0002-7665-476X, Fellner, K, Parsons, MJ et al. (1 more author) (2019) Growth behaviour of periodic tame friezes. Revista Matematica Iberoamericana, 35 (2). pp. 575-606. ISSN 0213-2230
Abstract
We examine the growth behaviour of the entries occurring in n-periodic tame friezes of real numbers. Extending work of the last author, we prove that generalised recursive relations exist between all entries of such friezes. These recursions are parametrised by a sequence of so-called growth coefficients, which is itself shown to satisfy a recursive relation. Thus, all growth coefficients are determined by a principal growth coefficient, which can be read-off directly from the frieze.
We place special emphasis on periodic tame friezes of positive integers, specifying the values the growth coefficients take for any such frieze. We establish that the growth coefficients of the pair of friezes arising from a triangulation of an annulus coincide. The entries of both are shown to grow asymptotically exponentially, while triangulations of a punctured disc are seen to provide the only friezes of linear growth.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2022 EMS Publishing House. All rights reserved. This is an author produced version of an article published in Revista Matemática Iberoamericana (RMI). Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Conway–Coxeter friezes, frieze patterns, finite friezes, infinite friezes, tame friezes, linear recursion, growth behaviour |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 10 Jan 2022 15:36 |
Last Modified: | 10 Jan 2022 15:36 |
Status: | Published |
Publisher: | EMS Press |
Identification Number: | 10.4171/rmi/1063 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:181776 |