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On the volume and projection of convex sets containing no lattice points

Published online by Cambridge University Press:  17 April 2009

P. R. Scott
P. R. Scott
Affiliation:
Department of Pure Mathematics, University of Adelaide, Adelaide, South Australia.
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Abstract

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A convex body K in En containing no lattice points, has one-deimensional projections of lengths X1, X2, …, Xn on the coordinate axes. We show that for n ≥ 2 and 1 ≤ Xi ≤ n/(n−1) (1 ≤ i ≤ n),

and this bound can not be improved.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 32 , Issue 3 , December 1985 , pp. 331 - 338
Copyright
Copyright © Australian Mathematical Society 1985

References

[1]Bonnesen, T., Fenchel, W., Theorie der konvexen Körper (Springer Verlag OHG, Berlin 1934; reprint Chelsea Publishing Company, New York 1948).Google Scholar
[2]Scott, P.R., “On simplices and lattice points”, J. Austral. Math. Soc. (Series A) 31 (1981), 15–19.CrossRefGoogle Scholar