# On partial well-order for monotone grid classes of permutations

## TL;DR

This paper provides a simplified proof that monotone grid classes of permutations, specifically those defined by forest structures, are partially well-ordered, contributing to the understanding of their structural properties.

## Contribution

It offers a simplified proof of partial well-ordering for monotone grid classes of forests, enhancing theoretical understanding of these permutation classes.

## Key findings

- Monotone grid classes of forests are partially well-ordered.
- Simplified proof of Murphy and Vatter's result.
- Structural properties of permutation classes clarified.

## Abstract

A monotone grid class is a permutation class (i.e., a downset of permutations under the containment order) defined by local monotonicity conditions. We give a simplified proof of a result of Murphy and Vatter that monotone grid classes of forests are partially well-ordered.