The exchange-graph conjecture for cluster algebras
The exchange-graph conjecture for cluster algebras
Let be a cluster algebra with initial exchange matrix . Its exchange graph is the quotient of the regular tree of seeds by simultaneous permutations of cluster variables, coefficients, and the rows and columns of the exchange matrix. Exchange-graph conjecture. The exchange graph of a cluster algebra depends only on the initial exchange matrix . This conjecture asserts that the exchange graph is independent of the chosen coefficients or realization of the cluster algebra, once is fixed. The supplied text gives no resolution status.
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Primary source
Michael Gekhtman, Michael Shapiro and Alek Vainshtein, “On the properties of the exchange graph of a cluster algebra”, arXiv:math/0703151 (2015).
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