A subset of a finite planar point set is called an empty convex polygon if it forms the set of vertices of a convex polygon whose interior contains no points of the set. Let Pbe a set of npoints in general position in the plane. An empty partition of Pis a partition of Pinto empty convex polygons. Let kbe a positive integer and  be the number of empty convex k-gons in an empty partition p of P. Denote  is an empty partition of      In this paper, we prove that  and further improve the lower bound of  to  For specified  we get the result that

convex hull, empty convex polygon, convex partition, disjoint partition, empty partition.