2 problems

Let $k$ be an integer with $k>1$, and let $\lambda$ be a partition. For the Ferrers board $B_\lambda$, let $R_k(\lambda;q)$ be its Garsia–Remmel $q$-rook number, and call this poly…

Garsia–Remmel's conjecture. For every partition $\lambda$ and every admissible rook number $k$, the polynomial $R_k(\lambda;q)$ has a unimodal sequence of coefficients. This conjec…