Ehrhart Polynomials of a Cyclic Polytopes

Abstract

Computing the volume of a polytope in Rn is a very important subject indifferent areas of mathematic. A pplications range from the very pure (number theory, toric Hilbert functions, Kostant's partition function in representation theory) to the most applied (cryptography, integer programming, contingency tables). In this work, the cyclic polytopes with some methods for finding their volumes are given. Moreover, the Ehrhart polynomial of cyclic polytope is computed with some methods. One of these methods is modified and gives a theorem for computing thecoefficients of the Ehrhart polynomials.