Isomorphisms between pattern classes
Michael Albert, M. D. Atkinson, Anders Claesson

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.
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