Title: Local Formulas for Ehrhart Coefficients from Lattice Tiles,
Abstract: As shown by McMullen in 1983, the coefficients of the Ehrhart polynomial of a
lattice polytope can be written as a weighted sum of facial volumes. The
weights in such a local formula depend only on the outer normal cones of faces,
but are far from being unique. In this paper, we develop an infinite class of
such local formulas. These are based on choices of fundamental domains in
sublattices and obtained by polyhedral volume computations. We hereby also give
a kind of geometric interpretation for the Ehrhart coefficients. Since our
construction gives us a great variety of possible local formulas, these can,
for instance, be chosen to fit well with a given polyhedral symmetry group. In
contrast to other constructions of local formulas, ours does not rely on
triangulations of rational cones into simplicial or even unimodular ones.