The paper provides a connection between Commutative Algebra and Integer Programming
and contains two parts. The first one is devoted to the asymptotic behavior of integer …

This book offers a gentle introduction to the geometry of numbers from a modern Fourier-
analytic point of view. One of the main themes is the transfer of geometric knowledge of a …

The Chow rank of a form is the length of its smallest decomposition into a sum of products of
linear forms. For a generic form, this corresponds to finding the smallest secant variety of the …

Parametric Presburger arithmetic concerns families of sets S_t in Z^ d, for t in N, that are
defined using addition, inequalities, constants in Z, Boolean operations, multiplication by t …

We show that the existential fragment of Büchi arithmetic is strictly less expressive than full
Büchi arithmetic of any base, and moreover establish that its Σ2-fragment is already …

This book is an introduction to the nascent field of Fourier analysis on polytopes, and cones.
There is a rapidly growing number of applications of these methods, so it is appropriate to …

Given a parametric lattice with a basis given by polynomials in Zt, we give an algorithm to
construct an LLL-reduced basis whose elements are eventually quasi-polynomial in t: that is …

Hurwitz numbers count genus g, degree d covers of the complex projective line with fixed
branched locus and fixed ramification data. An equivalent description is given by …

Given relatively prime positive integers a_1,..., a_n, the Frobenius number is the largest
integer that cannot be written as a nonnegative integer combination of the a_i. We examine …

Abstract Let f_1 (n), ..., f_k (n) f 1 (n),…, fk (n) be polynomial functions of n. For fixed n ∈ N
n∈ N, let S_n ⊆ NS n⊆ N be the numerical semigroup generated by f_1 (n), ..., f_k (n) f 1 …