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Journal of Algebraic Combinatorics

, Volume 30, Issue 3, pp 349–379 | Cite as

Frieze patterns for punctured discs

  • Karin Baur
  • Robert J. MarshEmail author
Article

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. This is generalised to arbitrary triangulations in an appendix by Hugh Thomas.

Keywords

Cluster algebra Frieze pattern Ptolemy rule Exchange relation Matching Riemann surface Disc Triangulation 

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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Department of MathematicsETH ZürichZürichSwitzerland
  2. 2.Department of Pure MathematicsUniversity of LeedsLeedsUK

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