On the classification of convex lattice polytopes (II)

In 1980, V. I. Arnold studied the classification problem for convex lattice polygons of given area. Since then this problem and its analogues have been studied by several authors, upper bounds for the numbers of non-equivalent d-dimensional convex lattice polytopes of given volume or fixed number of lattice points have been achieved. In this paper, by introducing and studying the unimodular groups acting on convex lattice polytopes, we obtain a lower bound for the number of non-equivalent d-dimensional centrally symmetric convex lattice polytopes of given number of lattice points, which is essentially tight.http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000334587600004&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=8e1609b174ce4e31116a60747a720701MathematicsSCI(E)0ARTICLEcmzong@math.pku.edu.cn2239-2521