The arithmetic of Coxeter permutahedra

Ehrhart theory measures a polytope $P$ discretely by counting the lattice points inside its dilates $P, 2P, 3P, \ldots$ . We compute the Ehrhart quasipolynomials of the standard Coxeter permutahedra for the classical Coxeter groups, expressing them in terms of the Lambert $W$ function. A central tool is a description of the Ehrhart theory of a rational translate of an integer zonotope. This is joint work with Federico Ardila (San Francisco State & Los Andes) and Jodi McWhirter (Washington University St. Louis).

Matthias Beck