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Séminaire Lotharingien de Combinatoire, 80B.96 (2018), 12 pp.

# Gleb Koshevoy

# Cluster Fan of **z**-Vectors and Toric Degenerations

**Abstract.**
For a cluster algebra, we introduce and study a notion of **z**-vectors.
We prove that **z**-vectors determine cluster variables. We
associate to a cluster seed a simplicial cone being span by
**z**-vectors of the cluster variables of this seed. These cones form a
fan, a polyhedral complex, such that the dual graph of this complex is
the Fomin-Zelevinsky exchange graph of the cluster algebra.

Received: November 14, 2017.
Accepted: February 17, 2018.
Final version: April 1, 2018.

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