Generalized permutahedra are an important class of polytopes which show up in many areas in mathematics. The volume and number of lattice points of these polytopes are given by certain multivariate polynomials that were introduced and studied by A. Postnikov, who further established various remarkable combinatorial properties thereof.  In this talk, I will discuss in depth the procedure of divided symmetrization that allows one to compute volumes of generalized permutahedra. Along the way, we will encounter familiar combinatorial objects such as standard Young tableaux, reduced pipe dreams, P-partitions and various Catalan objects.

This is joint work with Philippe Nadeau.