where a1, . . . , an are positive integers. This polytope is closely related to the linear Diophantine problem of Frobenius: given relatively prime positive integers a1, . . . , an, find the largest value of t (the Frobenius number) such that m1a1 + · · · + mnan = t has no solution in positive integers m1, . . . , mn. This is equivalent to the problem of finding the largest dilate tP such that ...

We discuss topics related to lattice points in rational polyhedra, including efficient enumeration of lattice points, “short” generating functions for lattice points in rational polyhedra, relations to classical and higher-dimensional Dedekind sums, complexity of the Presburger arithmetic, efficient computations with rational functions, and others. Although the main slant is algorithmic, struct...