Ehrhart polynomials of 3-dimensional simple integral convex polytopes

Abstract

The author gives an explicit formula on the Ehrhart polynomial of a 3-dimensional simple integral convex polytope by using toric geometry.

Keywords

Integral convex polytopes / Ehrhart polynomials / Toric geometry

References

[1] Beck M., Robins S.. Computing the Continuous Discretely, Undergraduate Texts in Mathematics, 2007, New York: Springer-Verlag

[2] Ehrhart E.. Polynômes Arithmétiques et Méthode des Polyèdres en Combinatoire, 1977

[3] Fulton, W., Introduction to Toric Varieties, Annals of Mathematics Studies, 131, Princeton Univ. Press, Princeton, NJ, 1993.

[4] Pommersheim J. E.. Toric varieties, lattice points and Dedekind sums. Math. Ann., 1993, 295: 1-24