Undergraduate Texts in Mathematics are generally aimed at third-and fourthyear
undergraduate mathematics students at North American universities. These texts strive to …

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 …

Triangulations presents the first comprehensive treatment of the theory of secondary
polytopes and related topics. The text discusses the geometric structure behind the …

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 …

Enumerative combinatorics has undergone enormous development since the publication of
the first edition of this book in 1986. It has become more clear what are the essential topics …

We present a practical algorithm for computing the volume of a convex body with a target
relative accuracy parameter ε> 0 ε> 0. The convex body is given as the intersection of an …

We experimentally study the fundamental problem of computing the volume of a convex
polytope given as an intersection of linear halfspaces. We implement and evaluate …

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 …

We present a new lower bound on the number of contingency tables, improving upon and
extending previous lower bounds by Barvinok [Bar09, Bar16] and Gurvits [Gur15]. As an …