Abstract
Certain classes of Schubert varieties are indexed by permutations in some permutation classes. In particular, permutations in A'=Av(52341,53241,52431,35142,42513,351624) index Schubert varieties that are local complete intersection.
Recently, Albert and Brignall discovered the generating function for the related class Av(4231,35142,42513,351624). Their method is based on constructing a regular language encoding the simple permutations in the class. This dissertation extends their method to enumerate the class A'.