We provide a comprehensive overview of the literature of algorithmic approaches for
multiobjective mixed‐integer and integer linear optimization problems. More precisely, we …

In Chapter 1, we have seen how the algebra of the polynomial rings k [x1,..., xn] and the
geometry of affine algebraic varieties are linked. In this chapter, we will study the method of …

The world is continuous, but the mind is discrete. David Mumford We seek to bridge some
critical gaps between various? elds of mathematics by studying the interplay between the …

During the early part of the last century, Ferdinand Georg Frobenius (1849-1917) raised he
following problem, known as the Frobenius Problem (FP): given relatively prime positive …

This paper discusses algorithms and software for the enumeration of all lattice points inside
a rational convex polytope: we describe LattE, a computer package for lattice point …

This is a self-contained exposition of several core aspects of the theory of rational polyhedra
with a view towards algorithmic applications to efficient counting of integer points, a problem …

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 …

This survey article is devoted to general results in combinatorial enumeration. The first part
surveys results on growth of hereditary properties of combinatorial structures. These include …

We consider discrete bilevel optimization problems where the follower solves an integer
program with a fixed number of variables. Using recent results in parametric integer …

A wide variety of topics in pure and applied mathematics involve the problem of counting the
number of lattice points inside a convex bounded polyhedron, for short called a polytope …