It is undeniable that geometric ideas have been very important to the foundations of modern
discrete optimization. The influence that geometric algorithms have in optimization was …

Emerging architectures, such as reconfigurable hardware platforms, provide the
unprecedented opportunity of customizing the memory infrastructure based on application …

The Todd polynomials $ td_k= td_k (b_1, b_2,\dots, b_m) $ are defined by their generating
functions $$\sum_ {k\ge 0} td_k s^ k=\prod_ {i= 1}^ m\frac {b_i s}{e^{b_i s}-1}. $$ It appears …

In this paper, we consider the counting function\({{\,\mathrm {{{\,\mathrm {\mathcal {E}}\,}} _
{{{\,\mathrm {\mathcal {P}}\,}}}}\,}}(y)=|{{\,\mathrm {\mathcal {P}}\,}} _ {y}\cap {{\,\mathrm …

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

We investigate properties of Ehrhart polynomials for matroid polytopes, independence
matroid polytopes, and polymatroids. In the first half of the paper we prove that, for fixed …

Presburger arithmetic is the first-order theory of the natural numbers with addition (but no
multiplication). We characterize sets that can be defined by a Presburger formula as exactly …

Let a polyhedron P be defined by one of the following ways: P={x∈ R n: A x≤ b}, where A∈
Z (n+ k)× n, b∈ Z (n+ k) and rank A= n, P={x∈ R+ n: A x= b}, where A∈ Z k× n, b∈ Z k and …

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 …

This paper presents a new methodology to compute the number of numerical semigroups of
given genus or Frobenius number. We apply generating function tools to the bounded …