On the properties of the exchange graph of a cluster algebra

Details On the properties of the exchange graph of a cluster algebra On the properties of the exchange graph of a cluster algebra

2007-03-06

arxiv.org/abs/math/0703151v1

Mathematics

Combinatorics

Scientific paper

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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