The convex hull of the integer points in a large ball

Abstract

where fk (P ) denotes the number of k–dimensional faces of the polytope P . The limit, as R → ∞, of the average of r−2/3f0(Pr ), on an interval [R,R + H ], is determined by Balog and Deshoullier [BD], and turns out to be 3.453 . . . , (H must be large). Our main result extends (1.1) to any d ≥ 2 and to any fk (Pr ) with k = 0, . . . , d − 1. Theorem 1. For every d ≥ 2 there are constants c1(d ) and c2(d ) such that for all k ∈ {0, . . . , d − 1}

1 Figure or Table

Cite this paper

@inproceedings{Brny1998TheCH, title={The convex hull of the integer points in a large ball}, author={Imre B{\'a}r{\'a}ny and David G. Larman}, year={1998} }