The main purpose of this book is to introduce algebraic, combinatorial, and computational
methods to study monomial algebras and their presentation ideals, including Stanley …

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

Page 1 WINFRIED BRUNS JOSEPH GUBELADZE Polytopes, Rings, and K-Theory Springer
Springer Monographs in Mathematics Page 2 Springer Monographs in Mathematics For further …

We are interested in the set of all subdivisions or triangulations of a given polytope P and
with a fixed finite set V of points that can be used as vertices. V must contain the vertices of …

It is a famous open question whether every integrally closed reflexive polytope has a
unimodal Ehrhart δ-vector. We generalize this question to arbitrary integrally closed lattice …

AMS eBooks: Memoirs of the American Mathematical Society Skip to Main Content
American Mathematical Society American Mathematical Society MathSciNet Bookstore …

We introduce the integrality number of an integer program (IP). Roughly speaking, the
integrality number is the smallest number of integer constraints needed to solve an IP via a …

We refer to the distance between optimal solutions of integer programs and their linear
relaxations as proximity. In 2018 Eisenbrand and Weismantel proved that proximity is …

In this article we overview those aspects of the theory of affine semigroups and their
algebras that have been relevant for our own research, and pose several open problems …

We consider the asymptotic distribution of the integer program (IP) sparsity function, which
measures the minimal support of optimal IP solutions, and the IP to linear program (LP) …