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On the properties of the exchange graph of a cluster algebra

Michael Gekhtman·Michael Shapiro·Alek Vainshtein
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Abstract

We prove a conjecture about the vertices and edges of the exchange graph of a cluster algebra $\A$ in two cases: when $\A$ is of geometric type and when $\A$ is arbitrary and its exchange matrix is nondegenerate. In the second case we also prove that the exchange graph does not depend on the coefficients of $\A$. Both conjectures were formulated recently by Fomin and Zelevinsky.

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Michael Gekhtman, Michael Shapiro, Alek Vainshtein. 2015-05-11. On the properties of the exchange graph of a cluster algebra. https://arxiv.org/abs/math/0703151

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