There has been significant work recently on integer programs (IPs) min {c⊤ x: A x≤ b, x∈ Z
n} with a constraint marix A with bounded subdeterminants. This is motivated by a well …

Consider a linear program of the form max {c⊤ x: A x≤ b}, where A is an m× n integral
matrix. In 1986 Cook, Gerards, Schrijver, and Tardos proved that, given an optimal solution …

Consider a matroid where all elements are labeled with an element in Z. We are interested
in finding a base where the sum of the labels is congruent to g (mod m). We show that this …

We study the maximal number of pairwise distinct columns in a Δ-modular integer matrix
with m rows. Recent results by Lee et al. provide an asymptotically tight upper bound of O (m …

An integer matrix is-modular if the determinant of each submatrix of has absolute value at
most. The study of-modular matrices appears in the theory of integer programming, where …

This paper deals with linear integer optimization. We develop a technique that can be
applied to provide improved upper bounds for two important questions in linear integer …

Motivated by complexity questions in integer programming, this paper aims to contribute to
the understanding of combinatorial properties of integer matrices of row rank $ r $ and with …

We study the lattice width of lattice-free polyhedra given by Ax≦b in terms of Δ(A), the
maximal n*n minor in absolute value of A∈Z^m*n. Our main contribution is to link the lattice …

Given a rational pointed-dimensional cone, we study the integer Carathéodory rank and its
asymptotic form, where we consider “most” integer vectors in the cone. The main result …

Consider a matroid equipped with a labeling of its ground set to an abelian group. We define
the label of a subset of the ground set as the sum of the labels of its elements. We study a …