Ptolemy relations for punctured discs
Combinatorics
2020-12-21 v1 Rings and Algebras
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.
Keywords
Cite
@article{arxiv.0711.1443,
title = {Ptolemy relations for punctured discs},
author = {Karin Baur and Bethany Marsh},
journal= {arXiv preprint arXiv:0711.1443},
year = {2020}
}
Comments
24 pages, 28 figures