The CDE property for minuscule lattices

摘要

Reiner, Tenner, and Yong recently introduced the coincidental down-degree expectations (CDE) property for finite posets and showed that many nice posets are CDE. In this paper we further explore the CDE property, resolving a number of conjectures about CDE posets put forth by Reiner Tenner Yong. A consequence of our work is the completion of a case-by-case proof that any minuscule lattice is ODE. We also explain two major applications of the study of ODE posets: formulas for certain classes of set-valued tableaux; and homomesy results for rowmotion and gyration acting on sets of order ideals. (C) 2017 Elsevier Inc. All rights reserved.