Algebras and Representation Theory

, Volume 22, Issue 1, pp 1–19 | Cite as

Cluster Expansion Formulas in Type A

  • Toshiya YurikusaEmail author


The aim of this paper is to give analogs of the cluster expansion formula of Musiker and Schiffler for cluster algebras of type A with coefficients arising from boundary arcs of the corresponding triangulated polygon. Indeed, we give three cluster expansion formulas by perfect matchings of angles in triangulated polygon, by discrete subsets of arrows of the corresponding ice quiver and by minimal cuts of the corresponding quiver with potential.


Cluster algebra Triangulation Perfect matching Quiver with potential 

Mathematics Subject Classfication (2010)

13F60 05C70 05E99 


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The author would like to thank his supervisor Osamu Iyama and Laurent Demonet for the helpful advice and instruction.


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Authors and Affiliations

  1. 1.Graduate School of MathematicsNagoya UniversityChikusa-kuJapan

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