Integer Knapsacks: Average Behavior of the Frobenius Numbers

• 成果类型: Article
• 署名作者: Aliev, Iskander; Henk, Martin
• 署名单位: Cardiff University; Cardiff University; Otto von Guericke University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.1090.0393
• 发表日期: 2009
• 页码: 698-705
• 关键词: linear diophantine problem; additive semigroups; lattice; bounds

摘要

The largest integer that cannot be represented as a nonnegative integral combination of given set of positive integers is called the Frobenius number of these integers. We show that the asymptotic growth of the Frobenius number on average is significantly slower than the growth of the maximum Frobenius number.