Geodesic
Frieze patterns for punctured discs
Journal of Algebraic Combinatorics, Tome 30 (2009) no. 3, pp. 349-379.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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: keywords cluster algebra, frieze pattern, Ptolemy rule, exchange relation, matching, Riemann surface, disc, triangulation 
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     author = {Baur, Karin and Marsh, Robert J.},
     title = {Frieze patterns for punctured discs},
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     url = {http://geodesic.mathdoc.fr/item/JAC_2009__30_3_a2/}
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Baur, Karin; Marsh, Robert J. Frieze patterns for punctured discs. Journal of Algebraic Combinatorics, Tome 30 (2009) no. 3, pp. 349-379. http://geodesic.mathdoc.fr/item/JAC_2009__30_3_a2/