Homomesy on stable set polytopes of paths

Homomesy is a phenomenon in which certain statistics have the same average over all orbits under some group action. We examine the rowmotion action on rational points in fractional stable set polytopes of path graphs, which can be viewed as a generalization of toggling on independent sets of paths. Our main theorem shows that for rational points in the fractional stable set polytope, the difference between the first and last coordinate averages to zero in all orbits of rowmotion. This is joint work with Ricky Liu.