# Characterising inflations of monotone grid classes of permutations

## TL;DR

This paper characterizes permutation classes with simple permutations that are monotone griddable by identifying nine key substructures, providing insights into the structural properties of these classes.

## Contribution

It introduces a novel characterization of permutation classes based on nine substructures, advancing understanding of monotone griddability in simple permutations.

## Key findings

- Identification of nine critical substructures in simple permutations.
- Characterization of classes with monotone griddable simple permutations.
- Structural conditions for the presence of long sums of 21s.

## Abstract

We characterise those permutation classes whose simple permutations are monotone griddable. This characterisation is obtained by identifying a set of nine substructures, at least one of which must occur in any simple permutation containing a long sum of 21s.