Enumeration of permutations indexing local complete intersection Schubert varieties

preprint2016arXivOpen access

Abstract

We find the generating function for the permutation class A′=Av(52341,53241,52431,35142,42513,351624)\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 A=Av(4231,35142,42513,351624)\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.

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