Abstract
In 1980, Arnold studied the classification problem for convex lattice polygons of given area. Since then this problem and its high dimensional analogue have been studied by Bárány, Pach, Vershik and others. Bounds for the number of non-equivalent d-dimensional convex lattice polytopes of given volume have been achieved. In this paper we study Arnold's problem for centrally symmetric lattice polygons and the classification problem for convex lattice polytopes of given cardinality. In the plane we obtain analogues to the bounds of Arnold, Bárány and Pach in both cases. However, the number of non-equivalent d-dimensional convex lattice polytopes of w lattice points is infinite whenever w – 1 ≥ d ≥ 3, which may intuitively contradict to Bárány and Vershik's upper bound.
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