English

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

R2 v1 2026-06-21T09:41:45.245Z