Flexible Schemes for Pattern-Avoiding Permutations

TL;DR

This paper enhances enumeration schemes to efficiently count a broad range of pattern-avoiding permutations, including those with regular insertion encodings, expanding the scope of combinatorial enumeration methods.

Contribution

It introduces modifications to existing enumeration schemes, enabling their application to new classes of pattern-avoiding permutations with regular insertion encodings.

Findings

Successfully enumerates new classes of pattern-avoiding permutations

Extends the applicability of enumeration schemes to regular insertion encoding classes

Provides a more efficient enumeration method for complex permutation classes

Abstract

We modify the enumeration schemes of Zeilberger and Vatter so that they can efficiently enumerate many new classes of pattern-avoiding permutations including all such classes with a regular insertion encoding.