Integral points in rational polygons: a numerical semigroup approach

Guadalupe Márquez-Campos; Jorge L. Ramírez-Alfonsín; José M. Tornero

doi:10.1007/s00233-016-9820-y

paper

Integral points in rational polygons: a numerical semigroup approach

arXiv:1907.01226 · doi:10.1007/s00233-016-9820-y

Abstract

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.