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Properties of axial diameters

Published online by Cambridge University Press:  17 April 2009

Paul R. Scott
Paul R. Scott
Affiliation:
Department of Mathematics, University of Adelaide, G.P.O. Box 498, Adelaide 5001, South Australia, Australia.
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Abstract

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Λ is a lattice and K a bounded, open, convex set in En. An axial diameter of K is the maximal length Xi, of chords of K parallel to the ith lattice basis vector (1 ≤ i ≤ n). A number of properties of the axial diameters are developed. For sets K containing just one lattice point, an inequality is established; when Λ is the integral lattice, this inequality takes the form .

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 39 , Issue 3 , June 1989 , pp. 329 - 333
Copyright
Copyright © Australian Mathematical Society 1989

References

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