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Friday, February 14, 2014

**Abstract:** Let G be a group acting with finite orbits on a set X, f any complex-valued function on X, and g the function on G-orbits given by averaging f. Surprisingly often, the function g turns out to be constant. In such cases, Propp and Roby say that the triple (X,G,f) exhibits combinatorial ergodicity (or homomesy). For rectangular semistandard tableaux under promotion, ergodicity was conjectured by Propp and Roby and proved by the speaker in joint work with J. Bloom and D. Saracino. We will discuss this result in the context of various other combinatorial examples of ergodicity.