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 …

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

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American Mathematical Society American Mathematical Society MathSciNet Bookstore …

In this paper we list a number of open problems and conjectures on Hilbert functions and
syzygies. Some of the problems are closely related to Algebraic Geometry, Combinatorics …

The integral closure can be describ ed geometrically. Let C (S) be the cone generated by S
in the vector space R n, ie, the set of all linear combinations of elements of S with non …

The first three sections of this survey represent an updated and much expanded version of
the abstract of my talk at FPSAC'2010: new results are incorporated and several concrete …

A submonoid of N d is of maximal projective dimension (MPD) if the associated affine
semigroup ring has the maximum possible projective dimension. Such submonoids have a …

An integer feasibility problem is a fundamental problem in many areas, such as operations
research, number theory, and statistics. To study a family of systems with no nonnegative …

In these notes we study combinatorial and algebraic properties of affine semigroups and
their algebras:(1) the existence of unimodular Hilbert triangulations and covers for normal …

Given an integral d× n matrix A, the well-studied affine semigroup S g (A)= b: A x= b, x∈ ℤ n,
x≥ 0 Sg (A)={b: Ax= b,\x ∈ Z^ n, x ≧ 0\} can be stratified by the number of lattice points …