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On simplices and lattice points

Part of: General convexity

Published online by Cambridge University Press:  09 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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Let S be a simplex in En which is homothetic to a given simplex S*, which contains no point of the integral lattice in its interior, and which has maximal volume V(S). We conjecture that V(S) > nn/n!, and establish the conjecture for n < 3.

MSC classification

Secondary: 52A20: Convex sets in $n$ dimensions (including convex hypersurfaces)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 31 , Issue 1 , June 1981 , pp. 15 - 19
Copyright
Copyright © Australian Mathematical Society 1981

References

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[5] Szekeres, G., ‘Note on lattice points within a parallelopiped’, J. London Math. Soc. 12 (1937), 36–39.Google Scholar