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.

Full Text
Published version (Free)

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call