We obtain residue formulae for certain functions of several vari-<lb>ables. As an application, we obtain closed formulae for vector partition func-<lb>tions and for their continuous analogs. They… (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)

This paper grew out of our efforts to understand the Toric Residue Mirror Conjecture formulated by Batyrev and Materov in [2]. This conjecture has its origin in Physics and is based on a work by… (More)

(with DF = 1 for F = P). As explained in [2], essential properties required on the operators DF are ”locality” and ”computability”. At each face F of P, the operator DF should depend only of the… (More)

We study intermediate sums, interpolating between integrals and discrete sums, which were introduced by A. Barvinok [Computing the Ehrhart quasi-polynomial of a rational simplex, Math. Comp. 75… (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)