The des-Wilf equivalence for two sets of West-2-stack-sortable patterns

For a permutation pattern $\tau$, let $F_n^{\operatorname{des}}(\tau;q)$ denote the descent generating polynomial over permutations in $\operatorname{Av}_n(\tau)$, and for sets of patterns let $F_n^{\operatorname{des}}(\Pi;q)$ be defined analogously. Write $\tau\equiv_{\operatorname{des}}\rho$ for equality of these polynomials for every $n$. The des-Wilf equivalence conjecture. The two sets of patterns satisfy

$$\{2341,\,3241\}\equiv_{\operatorname{des}}\{2413,\,3142\}.$$

The patterns in the left-hand set are the basis for the permutations that are West-$2$-stack-sortable, and the conjecture extends the paper's study of descent generating functions for avoidance classes. It is supported by the data considered in the paper, while no closed forms for the relevant functions are known.