The Fishburn-Wilf equivalence conjecture for patterns 2413, 2431 and 3241

Let $\mathscr{F}_n(\sigma)$ denote the set of Fishburn permutations of length $n$ avoiding the pattern $\sigma$. Fishburn-Wilf equivalence conjecture. The three pattern-avoidance classes are equinumerous:

$$\mathscr{F}_n(2413)\sim \mathscr{F}_n(2431)\sim \mathscr{F}_n(3241).$$

This conjecture is part of the paper's classification of Wilf equivalence classes for patterns of size four; the source gives no resolution, so its status remains open.