ON FINDING THE EHRHART POLYNOMIALS USING A MODIFIED PARTIAL FRACTION METHOD

A wide variety of topics in pure and applied mathematics involve the problem of counting the number of lattice points inside a polytope. Perhaps the most famous special case is the theory of Ehrhart polynomials, which is the basis structure theorem about this type of counting problem. We present a modified tool to find the Ehrhart polynomial of a convex polytope, by writing a polytope as a linear system and find the solution of this system using integer programming method with a modification on this method. This method depends on deriving the vector partition function as a partial fraction.