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

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...

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Bibliographic Details
Published in:International mathematics research notices 2020-01, Vol.2020 (1), p.71-90
Main Authors: Holm, Thorsten, Jørgensen, Peter
Format: Article
Language:English
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Summary: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.
ISSN:1073-7928
1687-0247
DOI:10.1093/imrn/rny020