On Some Conjectures by Rabinowitz

Abstract

Working on the problem of finding the numbers of lattice points inside convex lattice polygons, Rabinowitz has made several conjectures dealing with convex lattice nonagons and decagons. An intensive computer search preceded a formulation of the conjectures. The main purpose of this paper is to prove some of Rabinowitz’s conjectures. Moreover, we obtain an improvement of a conjectured result and give short proofs of two known results.