Letter graphs and geometric grid classes of permutations

TL;DR

This paper establishes an equivalence between geometric griddability of permutation classes and bounded lettericity of their inversion graphs, linking two structural concepts from graph theory and permutation patterns.

Contribution

It proves that geometric griddability of permutation classes is equivalent to bounded lettericity of their inversion graphs, connecting two previously unrelated notions.

Findings

Permutation classes are geometrically griddable iff their inversion graphs have bounded lettericity.

The work bridges structural graph theory and permutation pattern analysis.

Provides a new characterization of permutation classes through graph properties.

Abstract

We uncover a connection between two seemingly unrelated notions: lettericity, from structural graph theory, and geometric griddability, from the world of permutation patterns. Both of these notions capture important structural properties of their respective classes of objects. We prove that these notions are equivalent in the sense that a permutation class is geometrically griddable if and only if the corresponding class of inversion graphs has bounded lettericity.