Finding regular insertion encodings for permutation classes

TL;DR

This paper presents a practical algorithm and implementation for computing automata and generating functions for permutation classes with regular insertion encodings.

Contribution

It introduces an algorithm and Maple package that automate the computation of automata and rational generating functions for regular insertion encodings.

Findings

Algorithm successfully computes automata for regular insertion encodings.

Automated computation of rational generating functions achieved.

Implementation available in Maple package INSENC.

Abstract

We describe a practical algorithm which computes the accepting automaton for the insertion encoding of a permutation class, whenever this insertion encoding is regular. This algorithm is implemented in the accompanying Maple package INSENC, which can automatically compute the rational generating functions for such classes.