Publication details

Subpolygons in Conway-Coxeter frieze patterns

authored by
Michael Cuntz, Thorsten Holm
Abstract

Friezes with coefficients are maps assigning numbers to the edges and diagonals of a regular polygon such that all Ptolemy relations for crossing diagonals are satisfied. Among these, the classic Conway-Coxeter friezes are the ones where all values are positive integers and all edges have value 1. Every subpolygon of a Conway-Coxeter frieze yields a frieze with coefficients over the positive integers. In this paper we give a complete arithmetic criterion for which friezes with coefficients appear as subpolygons of Conway-Coxeter friezes. This generalizes a result of our earlier paper with Peter Jørgensen from triangles to subpolygons of arbitrary size.

Organisation(s)
Institute of Algebra, Number Theory and Discrete Mathematics
Type
Article
Journal
Algebraic Combinatorics
Volume
4
Pages
741-755
No. of pages
15
Publication date
02.09.2021
Publication status
Published
Peer reviewed
Yes
ASJC Scopus subject areas
Discrete Mathematics and Combinatorics
Electronic version(s)
https://doi.org/10.5802/ALCO.180 (Access: Open)