Proofs and generalizations of a homomesy conjecture of Propp and Roby

Jonathan Bloom, Oliver Pechenik, Dan Saracino

Let $G$ be a group acting on a set $X$ of combinatorial objects, with finite orbits, and consider a statistic $\xi :X\to \mathbb{C}$. Propp and Roby defined the triple $(X,G,\xi )$ t…