The CDE property for minuscule lattices

Abstract

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 CDE. We also explain two major applications of the study of CDE posets: formulas for certain classes of set-valued tableaux; and homomesy results for rowmotion and gyration acting on sets of order ideals.

52 pages, 9 figures; v2: minor updates

References in corpus (1)

• Poset edge densities, nearly reduced words, and barely set-valued tableaux

Cited by in corpus (6)

• On Order Ideals of Minuscule Posets III: The CDE Property
• Poset edge densities, nearly reduced words, and barely set-valued tableaux
• Minuscule doppelgängers, the coincidental down-degree expectations property, and rowmotion
• The CDE property for skew vexillary permutations
• Homomesy via Toggleability Statistics
• On the $q$-Enumeration of Barely Set-Valued Tableaux and Plane Partitions