Enumeration of permutations indexing local complete intersection Schubert varieties

TL;DR

This paper derives the generating function for a specific permutation class that indexes local complete intersection Schubert varieties, extending previous enumeration methods and completing the classification for these geometric objects.

Contribution

It introduces an extended enumeration method to find the generating function for a new permutation class related to Schubert varieties, completing the enumeration of all relevant classical classes.

Findings

Derived the generating function for the permutation class '

Extended enumeration techniques from previous work

Completed the enumeration of all classical classes indexing certain Schubert varieties

Abstract

We find the generating function for the permutation class $\mathcal{A}'=\text{Av}(52341,53241,52431,35142,42513,351624)$ whose permutations index local complete intersection Schubert varieties. The method we apply is the extension of how Albert and Brignall discover the generating function for $\mathcal{A}=\text{Av}(4231,35142,42513,351624)$ in their paper. This completes the enumerations of all classical permutation classes indexing certain types of Schubert varieties.