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Width-diameter relations for planar convex sets with lattice point constraints

Published online by Cambridge University Press:  17 April 2009

Poh W. Awyong  and
Paul R. Scott
Poh W. Awyong
Affiliation:
Department of Pure MathematicsThe University of AdelaideSouth Australia 5005Australia e-mail: pawyong@maths.adelaide.edu.aupscott@maths.adelaide.edu.au
Paul R. Scott
Affiliation:
Department of Pure MathematicsThe University of AdelaideSouth Australia 5005Australia e-mail: pawyong@maths.adelaide.edu.aupscott@maths.adelaide.edu.au
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Abstract

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We obtain an inequality concerning the width and diameter of a planar convex set with interior containing no point of the rectangular lattice. We then use the result to obtain a corresponding inequality for a planar convex set with interior containing exactly two points of the integral lattice.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 53 , Issue 3 , June 1996 , pp. 469 - 478
Copyright
Copyright © Australian Mathematical Society 1996

References

[1]Scott, P.R., ‘A lattice problem in the plane’, Mathematika 20 (1973), 247–252.CrossRefGoogle Scholar
[2]Scott, P.R., ‘Two inequalities for convex sets in the plane’, Bull. Austral. Math. Soc. 19 (1978), 131–133.CrossRefGoogle Scholar
[3]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
[4]Scott, P.R., ‘On planar convex sets containing one lattice point’, Quart. J. Maths. Oxford Ser. (2) 36 (1985), 105–111.CrossRefGoogle Scholar