On tropical dualities in cluster algebras

Details On tropical dualities in cluster algebras On tropical dualities in cluster algebras

2011-01-19

arxiv.org/abs/1101.3736v3

Contemp. Math. 565 (2012) 217--226

Mathematics

Rings and Algebras

10 pages; v2: expanded a little, an acknowledgment and reference added, minor editorial changes; v3: minor changes, final vers

Scientific paper

We study two families of integer vectors playing a crucial part in the structural theory of cluster algebras: the $\gg$-vectors parameterizing cluster variables, and the $\cc$-vectors parameterizing the coefficients. We prove two identities relating these vectors to each other. The proofs depend on the sign-coherence assumption for $\cc$-vectors that still remains unproved in full generality.

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