Introduces a piecewise-linear flow on cluster complexes whose leaves generalize green mutation, proving these complexes are spheres for Dynkin quivers and contractible for Euclidean quivers.
On tropical dualities in cluster algebras
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
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.
fields
math.RT 1years
2025 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
From green mutation to $\mathrm{X}$-evolution: flows and foliations on cluster complexes
Introduces a piecewise-linear flow on cluster complexes whose leaves generalize green mutation, proving these complexes are spheres for Dynkin quivers and contractible for Euclidean quivers.