Enumerating indices of Schubert varieties defined by inclusions

TL;DR

This paper extends grid classes to infinite grids to characterize simple permutations in a specific class, enabling enumeration and linking to algebraic geometry through Schubert varieties.

Contribution

It introduces a novel structural characterization of simple permutations in a pattern class related to Schubert varieties using infinite grid classes.

Findings

Structural characterization of simple permutations in the class.

Enumeration of the pattern class.

Connection established with algebraic geometry and Schubert varieties.

Abstract

By extending the notion of grid classes to include infinite grids, we establish a structural characterisation of the simple permutations in Av(4231, 35142, 42513, 351624), a pattern class which has three different connections with algebraic geometry, including the specification of indices of Schubert varieties defined by inclusions. This characterisation leads to the enumeration of the class.