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

2017/09/28 by Holm, Thorsten, Jorgensen, Peter · 2 citations
#05B45 #05E15 #05E99 #51M20 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1709.09861

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.

Cited by

• The Cyclic Sieving Phenomenon and frieze patterns
• On the construction of frieze patterns from partitions of convex polygons by nonintersecting diagonals

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