5 papers · 1 filter
Log-concavity and unimodality of cluster monomials in fan coordinates of type A_n
Zhichao Chen, Zhe Sun
We prove that every cluster monomial of type A_n is log-concave and unimodal with respect to its Laurent expansion in a fan initial cluster. We derive a coefficient formula for lam…
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…