Ptolemy relations for punctured discs

Abstract

We construct frieze patterns of type D_N with entries which are numbers of matchings between vertices and triangles of corresponding triangulations of a punctured disc. For triangulations corresponding to orientations of the Dynkin diagram of type D_N, we show that the numbers in the pattern can be interpreted as specialisations of cluster variables in the corresponding Fomin-Zelevinsky cluster algebra.

24 pages, 28 figures

References in corpus (1)

• The combinatorics of frieze patterns and Markoff numbers

Cited by in corpus (2)

• T-Path Formula and Atomic Bases for Cluster Algebras of Type D
• Geometric construction of cluster algebras and cluster categories