A p-angulated Generalisation of Conway and Coxeter's Theorem on Frieze Patterns

authored by

Thorsten Holm, Peter Jørgensen

Abstract

Coxeter defined the notion of frieze pattern, and Conway and Coxeter proved that triangulations of polygons are in bijection with integral frieze patterns. We show a p-angulated generalisation involving nonintegral frieze patterns. We also show that polygon dissections give rise to even more general nonintegral frieze patterns.

Organisation(s)

Institute of Algebra, Number Theory and Discrete Mathematics

External Organisation(s)

Newcastle University

Type

Article

Journal

International Mathematics Research Notices

Volume

2020

Pages

71-90

No. of pages

20

ISSN

1073-7928

Publication date

01.2020

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Mathematics(all)

Electronic version(s)

https://doi.org/10.48550/arXiv.1709.09861 (Access: Open)
https://doi.org/10.1093/imrn/rny020 (Access: Open)