Decidability in geometric grid classes of permutations

TL;DR

This paper demonstrates that for geometric grid classes of permutations, the basis and generating function can be effectively computed from the defining matrix using monadic second-order logic, advancing understanding of their structural properties.

Contribution

It introduces a method to compute the basis and generating function of geometric grid classes from the matrix using monadic second-order logic, providing new tools for permutation class analysis.

Findings

Basis and generating function are computable from matrix M.

Monadic second-order logic is effective for analyzing permutation classes.

Results apply to variations of geometric grid classes.

Abstract

We prove that the basis and the generating function of a geometric grid class of permutations Geom$(M)$ are computable from the matrix $M$, as well as some variations on this result. Our main tool is monadic second-order logic on permutations and words.