Frieze patterns for punctured discs
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.
Frieze2.pdf