论文标题
整数编程的渐近行为和Castelnuovo-Mumford的稳定性
Asymptotic behavior of Integer Programming and the stability of the Castelnuovo-Mumford regularity
论文作者
论文摘要
本文提供了交换代数和整数编程之间的联系，并包含两个部分。第一个专用于具有固定成本线性功能的整数程序的渐近行为，以及由有限的线性方程式系统或具有整数系数的不平等系统组成的约束集，该系统取决于$ n $。确定整数$ n _*$，以便这些整数程序的最佳功能是所有$ n \ ge n _*$的准线性函数。使用第一部分的结果，可以在第二部分绑定Castelnuovo-Mumford的稳定性指标，该稳定性是单体理想的整体闭合和无方形理想的符号力量的稳定性指标。
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 programs with a fixed cost linear functional and the constraint sets consisting of a finite system of linear equations or inequalities with integer coefficients depending linearly on $n$. An integer $N_*$ is determined such that the optima of these integer programs are a quasi-linear function of $n$ for all $n\ge N_*$. Using results in the first part, one can bound in the second part the indices of stability of the Castelnuovo-Mumford regularities of integral closures of powers of a monomial ideal and that of symbolic powers of a square-free monomial ideal.
