Frieze patterns for punctured discs

被引：20

作者：

Baur, Karin ^{[2
]}

Marsh, Robert J. ^{[1
]}

机构：

[1] Univ Leeds, Dept Pure Math, Leeds LS2 9JT, W Yorkshire, England

[2] ETH, Dept Math, CH-8092 Zurich, Switzerland

来源：

JOURNAL OF ALGEBRAIC COMBINATORICS | 2009年 / 30卷 / 03期

基金：

加拿大自然科学与工程研究理事会;

关键词：

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

D O I：

10.1007/s10801-008-0161-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：349 / 379

页数：31

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