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On the Number of Convex Lattice Polygons

Published online by Cambridge University Press:  12 September 2008

Imre Bárány  and
János Pach
Imre Bárány
Affiliation:
Cowles Foundation, Yale University, New Haven, CT 06520, USA; and Courant Institute, New York University, New York, NY 10012, USA
János Pach
Affiliation:
Courant Institute, New York University, New York, NY 10012, USA; and University College London, Gower Street, London WC1E 6BT, UK
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Abstract

We prove that there are at most {cA1/3} different lattice polygons of area A. This improves a result of V. I. Arnol'd.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 1 , Issue 4 , December 1992 , pp. 295 - 302
Copyright
Copyright © Cambridge University Press 1992

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References

[1]Andrews, G. E. (1976) The Theory of Partitions, Addison-Wesley.Google Scholar
[2]Andrews, G. E. (1965) A lower bound for the volumes of strictly convex bodies with many boundary points. Trans. Amer. Math. Soc. 106 270–279.Google Scholar
[3]Arnol'd, V. I. (1980) Statistics of integral lattice polygons (in Russian). Funk. Anal. Pril. 14 1–3.Google Scholar
[4]Konyagin, S. B. and Sevastyanov, K. A. (1984) Estimation of the number of vertices of a convex integral polyhedron in terms of its volume. Funk. Anal. Pril. 18 13–15.Google Scholar
[5]Rademacher, G. (1973) Topics in Analytic Number Theory, Springer.CrossRefGoogle Scholar
[6]Rényi, A. and Sulanke, R. (1933) Über die konvexe Hülle von n zufällig gewählten Punkten. Z. Wahrscheinlichkeitstheorie verw. Gebiete x 375–84.Google Scholar
[7]Schmidt, W. (1985) Integer points on curves and surfaces. Monatshefte Math. 99 45–82.Google Scholar
[8]Szekeres, G. (1951) On the theory of partitions. Quarterly J. Math. Oxford, Second Series 2 85–108.CrossRefGoogle Scholar