Asymptotic behavior of integer programming and the stability of the Castelnuovo-Mumford regularity

• 成果类型: Article
• 署名作者: Hoa, Le Tuan
• 署名单位: Vietnam Academy of Science & Technology (VAST)
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-020-01595-x
• 发表日期: 2022
• 页码: 157-194
• 关键词: geometrie diophantienne lineaire; sur un probleme; edge ideals; POWERS; stabilization; closures

摘要

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 >= 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.