Zhi-Chao Chen

Log-concavity and unimodality of cluster monomials in fan coordinates of type $A_n$

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 laminar interval products arising from compatible diagonals in the polygon model. In even rank, we reduce log-concavity in fan coordinates to...