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For a set of permutation patterns $\Pi$, let $F^\text{st}_n(\Pi,q)$ be thest-polynomial of permutations avoiding all patterns in $\Pi$. Suppose$312\in\Pi$. For a class of permutation statistics which includes inversion anddescent statistics, we give a formula that expresses $F^\text{st}_n(\Pi;q)$ interms of these st-polynomials where we take some subblocks of the patterns in$\Pi$. Using this formula, we can construct many examples of nontrivial st-Wilfequivalences. In particular, this disproves a conjecture by Dokos, Dwyer,Johnson, Sagan, and Selsor that all $\text{inv}$-Wilf equivalences are trivial.

Permutation Statistics and Multiple Pattern Avoidance