7 papers
Log-concavity and unimodality of cluster monomials in fan coordinates of type
Zhichao Chen, Zhe Sun
We prove that every cluster monomial of type is log-concave and unimodal with respect to its Laurent expansion in a fan initial cluster. We derive a coefficient formula for l…
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…
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…
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…
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…