Bijections for generalized Wilf equivalences

TL;DR

This paper introduces a recursive bijection method to prove generalized Wilf equivalences among consecutive patterns in inversion sequences, providing new and direct combinatorial proofs for existing and stronger relations.

Contribution

It presents a recursive subtraction technique to construct direct bijections for generalized Wilf equivalences, enhancing combinatorial proof methods.

Findings

Established bijections for several generalized Wilf equivalences

Provided new combinatorial proofs for stronger pattern relations

Extended the methodology to a broader class of identities

Abstract

Starting with an inclusion-exclusion proof of a combinatorial identity, a direct bijection can be produced using recursive subtraction (sometimes with a direct combinatorial description). We apply this method to identities for generalized Wilf equivalences among consecutive patterns in inversion sequences, giving direct bijective proofs of some generalized Wilf equivalences shown by Auli and Elizalde. We also give new bijective proofs of a stronger relation among some consecutive patterns.