Title
Doppelgängers: bijections of plane partitions
Department/School
Mathematics
Date
3-13-2018
Document Type
Article
Abstract
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 of R. Proctor. Geometrically, these bijections reflect the rational equivalence of certain subvarieties of minuscule flag manifolds. As a special case, we provide the first bijective proof of a 1983 theorem of R. Proctor---that plane partitions of height k in a rectangle are equinumerous with plane partitions of height k in a trapezoid.
Published in
International Mathematics Research Notices
Citation/Other Information
Hamaker, Z., Patrias, R., Pechenik, O., Williams, N. (2018). Doppelgängers: Bijections of Plane Partitions, International Mathematics Research Notices, Volume 2020(2): 487–540, https://doi.org/10.1093/imrn/rny018.