Integral points in rational polygons: a numerical semigroup approach

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• 作者：Guadalupe Márquez-Campos ; Jorge L. Ramírez-Alfonsín ; José M. Tornero
• 关键词：Lattice points ; Numerical semigroups ; Geometry of numbers
• 刊名：Semigroup Forum
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：94
• 期：1
• 页码：123-138
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Algebra;
• 出版者：Springer US
• ISSN：1432-2137
• 卷排序：94

文摘

In this paper we use an elementary approach by using numerical semigroups (specifically, those with two generators) to give a formula for the number of integral points inside a right-angled triangle with rational vertices. This is the basic case for computing the number of integral points inside a rational (not necessarily convex) polygon.