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Doppelgängers: Bijections of Plane Partitions
We say two posets are "doppelgängers" if they have the same number of $P$-partitions of each height $k$. We give a uniform framework for bijective proofs that posets are doppelgängers by synthesizing $K$-theoretic Schubert calculus techniques of H. Thomas and A. Yong with M. Haiman's rectification bijection and an observation …