Subpolygons in Conway-Coxeter frieze patterns

verfasst von

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.

Organisationseinheit(en)

Institut für Algebra, Zahlentheorie und Diskrete Mathematik

Typ

Artikel

Journal

Algebraic Combinatorics

Band

4

Seiten

741-755

Anzahl der Seiten

15

Publikationsdatum

02.09.2021

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Diskrete Mathematik und Kombinatorik

Elektronische Version(en)

https://doi.org/10.5802/ALCO.180 (Zugang: Offen)