3 problems

Let $F_s(q)$ be defined by … and, for $s\ge 2$, … Let $EN_{s,t}(\sigma)(q)$ denote the inversion-generating function for pattern-avoiding linear extensions of the rectangular poset…

Let $m=8+12q$ with $q=61+64d$ for some nonnegative integer $d$. Define the sequence $\{g_l\}_{l\ge 10}$ as in the preceding definition, with $g_{10}$ and $g_{10}'$ selected accordi…

The coefficient-of-$q^{2s-2}$ conjecture. For all $s\ge2$, the coefficient of $q^{2s-2}$ in $F_s(q)$ is the number of compositions of $s+9$ into $s$ parts, none of which is $2$ or…