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A note on bounds on the minimum area of convex lattice polygons

Published online by Cambridge University Press:  17 April 2009

Charles J. Colbourn  and
R.J. Simpson
Charles J. Colbourn
Affiliation:
School of Mathematics and Statistics Curtin University of TechnologyGPO Box U 1987 Perth WA 6001, Australia
R.J. Simpson
Affiliation:
School of Mathematics and Statistics Curtin University of TechnologyGPO Box U 1987 Perth WA 6001, Australia
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Abstract

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The minimum area a(v) of a v–sided convex lattice polygon is known to satisfy . We conjecture that a(v) = cv3 + o(v3), for c a constant; we prove that , and that for some positive constant c, .

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 45 , Issue 2 , April 1992 , pp. 237 - 240
Copyright
Copyright © Australian Mathematical Society 1992

References

[1]Arkinstall, J.R., ‘Minimal requirements for Minkowski's theorem in the plane I’, Bull. Austral. Math. Soc. 22 (1980), 259–274.CrossRefGoogle Scholar
[2]Rabinowitz, S., ‘On the number of lattice points inside a convex lattice n–gon’, Congr. Numer. 73 (1990), 99–124.Google Scholar
[3]Simpson, R.J., ‘Convex lattice polygons of minimum area’, Bull. Austral. Math. Soc. 42 (1990), 353–367.CrossRefGoogle Scholar