  We establish a connection between the orbifold cohomology of hypertoric
varieties and the Ehrhart theory of Lawrence polytopes. More specifically, we
show that the dimensions of the orbifold cohomology groups of a hypertoric
variety are equal to the coefficients of the Ehrhart $\delta$-polynomial of the
associated Lawrence polytope. As a consequence, we deduce a formula for the
Ehrhart $\delta$-polynomial of a Lawrence polytope and use the injective part
of the Hard Lefschetz Theorem for hypertoric varieties to deduce some
inequalities between the coefficients of the $\delta$-polynomial.

Combinatorics;Algebraic Geometry