We obtain residue formulae for certain functions of several variables. As an application, we obtain closed formulae for vector partition functions and for their continuous analogs. They imply an… (More)

ANDR´AS SZENES AND MICH`ELE VERGNE 0. Introduction This paper grew out of an attempt to understand a conjecture formulated by Batyrev and Materov in [2]. The conjecture has its origin in Physics and… (More)

Consider the space R∆ of rational functions of r variables with poles on an arrangement of hyperplanes ∆. It is important to study the decomposition of the space R∆ under the action of the ring of… (More)

This paper settles the computational complexity of the problem of integrating a polynomial function f over a rational simplex. We prove that the problem is NP-hard for arbitrary polynomials via a… (More)

P (h) φ(x)dx where the polytope P (h) is obtained from P by independent parallel motions of all facets. This extends to simple lattice polytopes the EulerMaclaurin summation formula of Khovanskii and… (More)

where b(n) are the Bernoulli numbers. When p is an integral polytope, the existence of such operators is the combinatorial counterpart of a homological property of the associated toric variety: the… (More)

This article concerns the computational problem of counting the lattice points inside convex polytopes, when each point must be counted with a weight associated to it. We describe an efficient… (More)