Abstract
We construct frieze patterns of type DN 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 DN, 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.
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Acknowledgements
The author was supported by an NSERC Discovery Grant. The appendix was written during a visit to NTNU; he thanks the Institutt for Matematiske Fag for its hospitality. He would also like to thank Bethany R. Marsh and Karin Baur for their comments on the original draft of this appendix.
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The authors were supported by an EPSRC grant, number GR/S35387/01.
With an Appendix by Hugh Thomas.
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Baur, K., Marsh, B.R. Frieze patterns for punctured discs. J Algebr Comb 30, 349–379 (2009). https://doi.org/10.1007/s10801-008-0161-0
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DOI: https://doi.org/10.1007/s10801-008-0161-0