Zhichao Chen

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20242026

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math.RT2026

Log-concavity and unimodality of cluster monomials of type $A_{3}$

Zhichao Chen

The log-concavity of cluster variables of type $A_{n}$ and cluster monomials of type $A_{2}$ was established by Chen-Huang-Sun. It is still a conjecture for the cluster monomials of hi…

math.RT2026

Fractal phenomenon in $c$ - and $g$ -vectors of the Markov quiver

Ryota Akagi, Zhichao Chen

We study the $C$ - and $G$ -patterns associated with rank $3$ skew-symmetrizable matrices of $B$ -invariant type, including the Markov quiver. Motivated by the self-contained simple m…

math.RT2024

Log-concavity of cluster algebras of type $A_{n}$

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…

Log-concavity and unimodality of cluster monomials of type A3​

Fractal phenomenon in c- and g-vectors of the Markov quiver

Log-concavity of cluster algebras of type An​

Log-concavity and unimodality of cluster monomials of type $A_{3}$

Fractal phenomenon in $c$ - and $g$ -vectors of the Markov quiver

Log-concavity of cluster algebras of type $A_{n}$