Integral points in rational polygons: a numerical semigroup approach

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 r...

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Bibliographic Details
Published inSemigroup forum Vol. 94; no. 1; pp. 123 - 138
Main Authors Márquez-Campos, Guadalupe, Ramírez-Alfonsín, Jorge L., Tornero, José M.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.02.2017
Springer Nature B.V
Springer Verlag
Subjects
Algebra
Integrals
Mathematics
Mathematics and Statistics
Polygons
Research Article
Numerical semigroups
Geometry of numbers
Lattice points
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Summary: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.
ISSN:0037-1912
1432-2137
DOI:10.1007/s00233-016-9820-y