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Cluster Expansion Formulas in Type A

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Abstract

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.

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Acknowledgements

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. Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya, 464-8602, Japan

    Toshiya Yurikusa

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  1. Toshiya Yurikusa
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Correspondence to Toshiya Yurikusa.

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Presented by Steffen Koenig.

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Yurikusa, T. Cluster Expansion Formulas in Type A. Algebr Represent Theor 22, 1–19 (2019). https://doi.org/10.1007/s10468-017-9755-3

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  • DOI: https://doi.org/10.1007/s10468-017-9755-3

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Mathematics Subject Classfication (2010)

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