Unified framework for arrow-Wilf equivalence

Develop a unified framework for arrow-Wilf equivalence that explains the equivalences currently obtained through ad hoc arguments, including those arising from reversal, complementation, and insertion operations.

Background

Arrow-Wilf equivalence compares arrow patterns whose avoidance classes have equal cardinalities in every permutation length. The paper proves several such equivalences using reversal, complementation, insertion, and specialized bijections.

The authors note that these proofs are ad hoc and explicitly leave unresolved whether a more systematic theory can account for them. A general framework would organize the known equivalences and potentially produce additional ones.