Speaker: Nathan Williams

Title: Doppelgängers and Bijections of Plane Partitions

 

For certain root posets, there exists a "doppelgänger" minuscule poset---that is, both posets have the same number of linear extensions and the same number of plane partitions of height k.  In these cases, there happens to also be a second minuscule poset whose top half is the root poset. These two facts are related.

 

We synthesize M. Haiman's rectification, H. Thomas and A. Yong's minuscule K-theoretic Schubert calculus techniques, and a remark made by R. Proctor to give a framework for combinatorial proofs of these poset coincidences.

 

This is joint work with Zachary Hamaker, Rebecca Patrias, and Oliver Pechenik.