Enumeration schemes for restricted permutations

TL;DR

This paper extends Zeilberger's enumeration schemes to cover more permutation classes and introduces the Maple package WILFPLUS, comparing its effectiveness with other enumeration methods.

Contribution

The authors expand enumeration schemes to a broader range of permutation classes and develop the WILFPLUS software for automated enumeration.

Findings

WILFPLUS successfully automates enumeration for many new permutation classes

Enumeration schemes outperform some existing methods in certain classes

Comparison shows strengths and limitations of different enumeration techniques

Abstract

Zeilberger's enumeration schemes can be used to completely automate the enumeration of many permutation classes. We extend his enumeration schemes so that they apply to many more permutation classes and describe the Maple package WILFPLUS, which implements this process. We also compare enumeration schemes to three other systematic enumeration techniques: generating trees, substitution decompositions, and the insertion encoding.