On the effective and automatic enumeration of polynomial permutation classes

TL;DR

This paper presents a Python algorithm that automatically enumerates permutation classes with polynomial growth, enabling the derivation of formulas for permutation counts under various block sorting operations.

Contribution

It introduces a novel algorithm for the automatic enumeration of permutation classes with polynomial enumeration from structural descriptions.

Findings

Successfully enumerates classes with polynomial growth

Derives formulas for permutations under block sorting operations

Implemented in Python for practical use

Abstract

We describe an algorithm, implemented in Python, which can enumerate any permutation class with polynomial enumeration from a structural description of the class. In particular, this allows us to find formulas for the number of permutations of length n which can be obtained by a finite number of block sorting operations (e.g., reversals, block transpositions, cut-and-paste moves).