The exchange-graph conjecture for cluster algebras

From papers

Let A{\mathcal A} be a cluster algebra with initial exchange matrix BB. 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 BB. This conjecture asserts that the exchange graph is independent of the chosen coefficients or realization of the cluster algebra, once BB is fixed. The supplied text gives no resolution status.

Progress summary

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Sources & referencesView supporting material

Primary source

Michael Gekhtman, Michael Shapiro and Alek Vainshtein, “On the properties of the exchange graph of a cluster algebra”, arXiv:math/0703151 (2015).

Solutions 0

No solutions have been posted yet.