2 problems

Let $G_s(n,k)$ be the recurrence obtained by summing over partitions of $k$ having size at most $s$, with $q$ an indeterminate and $n,k,s$ in the domain where this recurrence is de…

For $n\geqslant 2$, define … where $[m]!=(1-q)(1-q^2)\cdots(1-q^m)$. Unimodality conjecture. The polynomial $P_n(q)$ is unimodal. The polynomial is known to be reciprocal, and the…