On tropical dualities in cluster algebras
arXiv:1101.3736
Abstract
We study two families of integer vectors playing a crucial part in the structural theory of cluster algebras: the -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.
10 pages; v2: expanded a little, an acknowledgment and reference added, minor editorial changes; v3: minor changes, final version, to appear in Proceedings of Representation Theory of Algebraic groups and Quantum groups, 10, Contemp. Math., AMS
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