Hostname: page-component-8448b6f56d-42gr6 Total loading time: 0 Render date: 2024-04-16T19:16:04.101Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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