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 …

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 …

The Frobenius number g (A) of a set A=(a1, a2,..., an) of positive integers is the largest
integer not representable as a nonnegative linear combination of the ai. We interpret the …

We study the computational complexity of short sentences in Presburger arithmetic (Short-
PA). Here by “short” we mean sentences with a bounded number of variables, quantifiers …

We settle the computational complexity of fundamental questions related to multicriteria
integer linear programs, when the dimensions of the strategy space and of the outcome …

If P is a rational polytope in R^ d, then $ i_P (t):=#(tP\cap Z^ d) $ is a quasi-polynomial in t,
called the Ehrhart quasi-polynomial of P. A period of i_P (t) is D (P), the smallest positive …

barvinok: User Guide Page 1 barvinok: User Guide Version: barvinok-0.39 Sven
Verdoolaege January 15, 2016 Contents Contents 1 1 isl interface 5 1.1 Library …

Motivated by the formula for the sum of the geometric series, we consider various classes of
sets S⊂ Zd of integer points for which an a priori “long” Laurent series or polynomial∑ m∈ …

We study complexity of short sentences in Presburger arithmetic (Short-PA). Here by “short”
we mean sentences with a bounded number of variables, quantifers, inequalities and …