Ptolemy relations for punctured discs

Karin Baur and Bethany Marsh
Arxiv ID: 0711.1443Last updated: 12/21/2020
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.

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