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Minimal width and diameter of lattice-point-free convex bodies

Published online by Cambridge University Press:  26 February 2010

P. McMullen  and
J. M. Wills
P. McMullen
Affiliation:
Department of Mathematics, University College, Gower Street, London WC1E 6BT.
J. M. Wills
Affiliation:
Universität Siegen, Fach bereich 6, Mathematik, 5900 Siegen 21, Hölderlinstrasse 3, West Germany.
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Extract

Let K be a convex body (compact convex set with interior points) in d-dimensional euclidean space Ed, let D(K) denote its diameter, Δ(K) its minimal width, and

the number of lattice points (points of Ed with integer coordinates) in the interior of K. If G0(K) = 0, we call K lattice-point-free; in what follows, K will always be a lattice-point-free convex body.

Type
Research Article
Information
Mathematika , Volume 28 , Issue 2 , December 1981 , pp. 255 - 264
Copyright
Copyright © University College London 1981

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References

1.Bonnesen, T. and Fenchel, W.. Theorie der konvexen Körper (Springer, Berlin, 1934).Google Scholar
2.Coxeter, H. S. M.. Regular Polytopes (Dover, New York, 1973).Google Scholar
3.Danzer, L., Laugwitz, D. and Lenz, H.. “Über das Löwnersche Ellipsoid und sein Analogon unter den einem Eikörper einbeschriebenen Ellipsoiden”, Arch. Math., 8 (1957), 214–219.CrossRefGoogle Scholar
4.Scott, P. R.. “A lattice problem in the plane”, Mathematika, 20 (1973), 247–252.CrossRefGoogle Scholar
5.Scott, P. R.. “Two inequalities for convex sets with lattice point constraints in the plane”, Bull. London Math. Soc., 11 (1979), 273–278.CrossRefGoogle Scholar