Pattern classes and priority queues

TL;DR

This paper investigates how pattern classes behave under priority queue operations, determining the basis of the resulting class for certain cases and providing examples of classes with infinite bases.

Contribution

It characterizes the basis of output pattern classes after priority queue processing for classes with basis elements of length 3 and presents an example with an infinite basis.

Findings

Basis of C' is finite when C's basis elements have length 3

Explicit basis determination for certain pattern classes

Example of a class with an infinite basis

Abstract

When a set of permutations comprising a pattern class C is submitted as input to a priority queue the resulting output is again a pattern class C'. The basis of C' is determined for pattern classes C whose basis elements have length 3, and is finite in these cases. An example is given of a class C with basis 2431 for which C is not finitely based.