Half-open integer parallelepipeds and polytope Dedekind sums

Sinai Robins, André Rosenbaum Coelho

We study the Ehrhart theory of half-open $d$-dimensional integer parallelepipeds $\Pi$. Although the lattice-point count $t\Pi \cap {\mathbb{Z}}^d$ is known to be simply $\vol Πt^d$ for positive…