On the inverse image of pattern classes under bubble sort

TL;DR

This paper investigates the conditions under which the inverse image of a pattern class, after applying one pass of bubble sort, remains a pattern class, providing a complete characterization.

Contribution

It provides a complete characterization of when the inverse image of a principal pattern class under bubble sort is itself a pattern class.

Findings

Identifies conditions for inverse images to be pattern classes

Provides a complete answer for principal pattern classes

Advances understanding of pattern classes under sorting operations

Abstract

Let B be the operation of re-ordering a sequence by one pass of bubble sort. We completely answer the question of when the inverse image of a principal pattern class under B is a pattern class.