2 problems

Let $S_{n,k}$ be the triangle defined by … for $1\leq k\leq n-2$, with $S_{n,n}=S_{n,n-1}=S_{n,n-2}$ for $n\geq 3$ and $S_{1,1}=S_{2,1}=S_{2,2}=1$. For a pair of patterns…

Let $\text{SC}_{\underline{23}1}$ be the vincular-pattern-avoiding stack-sorting map, let $\text{Sort}_n(\text{SC}_{\underline{23}1})$ denote its sorting class in $\mathfrak S_n$,…