Isomorphisms between pattern classes

TL;DR

This paper investigates isomorphisms between pattern classes, showing that non-symmetry isomorphisms imply that one class is contained within a small, well-structured set of classes with known enumeration.

Contribution

It characterizes the structure of pattern class isomorphisms, revealing that non-symmetry cases lead to classes within a limited, well-understood set.

Findings

Non-symmetry isomorphisms imply subset relations.

The structure and enumeration of these classes are determined.

A small set of pattern classes encompasses all such cases.

Abstract

Isomorphisms p between pattern classes A and B are considered. It is shown that, if p is not a symmetry of the entire set of permutations, then, to within symmetry, A is a subset of one a small set of pattern classes whose structure, including their enumeration, is determined.