Ehrhart polynomials of 3-dimensional simple integral convex polytopes

TL;DR

This paper derives an explicit formula for the Ehrhart polynomial of 3-dimensional simple integral convex polytopes using tools from toric geometry, providing a new computational approach.

Contribution

It introduces a novel explicit formula for Ehrhart polynomials of 3D simple integral convex polytopes based on toric geometry techniques.

Findings

Explicit formula for Ehrhart polynomial derived

Utilizes toric geometry for computation

Advances understanding of lattice point enumeration

Abstract

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