Combinatorics, Probability and Computing

Research Article

On the Number of Convex Lattice Polygons

Imre Báránya1 and János Pacha2

a1 Cowles Foundation, Yale University, New Haven, CT 06520, USA; and Courant Institute, New York University, New York, NY 10012, USA

a2 Courant Institute, New York University, New York, NY 10012, USA; and University College London, Gower Street, London WC1E 6BT, UK

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.

(Received December 06 1991)

(Revised September 18 1992)

Footnotes

On leave from the Mathematical Institute of the Hungarian Academy of Sciences, POB 127, 1364 Budapest, Hungary. Supported by the Program in Discrete Mathematics and its Applications at Yale, NSF grant CCR–8901484, and Hungarian NSF grant nos. 1907 and 1909

On leave from the Mathematical Institute of the Hungarian Academy of Sciences, POB127, 1364 Budapest, Hungary. Supported by NSF grant CCR–8901484, and Hungarian NSF grant nos. 1907 and 1909.