Leírás
In this talk I will explain a connection between Commutative
Algebra and Linear and Integer Programming. In the first part, it is
explained how one can translate the problem of bounding the index of
stability of the Castelnuovo-Mumford regularities of the integral
closures of powers of a monomial ideal into an Integer Linear
Programming. The second part is devoted to the asymptotic behavior of
Linear and Integer Programming with a fixed cost linear functional and
the constraint sets consisting of a finite system of linear equations or
inequalities with integral coefficients depending linearly on $n$. It is
shown that the optima of such Linear Programming problems are a linear
function of $n$, while the optima of the corresponding Integer
Programming problems are a quasi-linear function of $n$, provided $n\gg
0$. In the last part I give bounds on the indices of stability of the
Castelnuovo-Mumford regularities of the integral closures of powers of a
monomial ideal and that of symbolic powers of a square-free monomial
ideal.