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

  • P. R. Scott (a1)

Abstract

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 n2 and 1Xin/(n1) (1in),

and this bound can not be improved.

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Copyright

References

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[1]Bonnesen, T., Fenchel, W., Theorie der konvexen Körper (Springer Verlag OHG, Berlin 1934; reprint Chelsea Publishing Company, New York 1948).
[2]Scott, P.R., “On simplices and lattice points”, J. Austral. Math. Soc. (Series A) 31 (1981), 1519.
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On the volume and projection of convex sets containing no lattice points

  • P. R. Scott (a1)

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