A $p$-angulated generalisation of Conway and Coxeter's theorem on frieze patterns

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 non-integral frieze patterns. We also show that polygon dissections give rise to even more general non-integral frieze patterns.

This is the final accepted version. It was accepted for publication by the International Mathematics Research Notices on 23/1-2018. 14 pages