6 papers
Mutation-preserving generalized cluster algebras and Laurent mutation invariants
Zhichao Chen, Yimin Huang
We introduce mutation-preserving generalized cluster algebras, for which the generalized cluster mutation in each direction is independent of the seed in the mutation equivalence c…
Log-concavity and unimodality of cluster monomials of type
Zhichao Chen
The log-concavity of cluster variables of type and cluster monomials of type was established by Chen-Huang-Sun. It is still a conjecture for the cluster monomials of hi…
Fractal phenomenon in - and -vectors of the Markov quiver
Ryota Akagi, Zhichao Chen
We study the - and -patterns associated with rank skew-symmetrizable matrices of -invariant type, including the Markov quiver. Motivated by the self-contained simple m…
The Logarithmic Asymptotic Phenomenon for Generalized Markov-Hurwitz Equations
Zhichao Chen, Zelin Jia, Wenchao Wu
The purpose of this paper is twofold. First, we introduce a family of generalized Markov-Hurwitz equations, extending classical Markov-Hurwitz equations with additional degree n-1…
Tropicalization and cluster asymptotic phenomenon of generalized Markov equations
Zhichao Chen, Zelin Jia
The generalized Markov equations are deeply connected with the generalized cluster algebras of Markov type. We construct a deformed Fock-Goncharov tropicalization for the generaliz…
Log-concavity of cluster algebras of type
Zhichao Chen, Guanhua Huang, Zhe Sun
Okounkov [Oko03] conjectured the log-concavity about the structure constants for many interesting basis from representation theory. For the cluster algebra, Gross, Hacking, Keel, K…