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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Bárány, I. and Yuan, L. 2014. Volumes of Convex Lattice Polytopes and A Question of V. I. Arnold. Acta Mathematica Hungarica, Vol. 144, Issue. 1, p. 119.


    Bárány, Imre 2012. On a question of V. I. Arnol’d. Acta Mathematica Hungarica, Vol. 137, Issue. 1-2, p. 72.


    Dumitrescu, Adrian and Jiang, Minghui 2012. Minimum-Perimeter Intersecting Polygons. Algorithmica, Vol. 63, Issue. 3, p. 602.


    Shparlinski, Igor E. 2012. Modular hyperbolas. Japanese Journal of Mathematics, Vol. 7, Issue. 2, p. 235.


    Liu, Heling and Zong, Chuanming 2011. On the classification of convex lattice polytopes. Advances in Geometry, Vol. 11, Issue. 4,


    Schicho, Josef 2003. Simplification of surface parametrizations—a lattice polygon approach. Journal of Symbolic Computation, Vol. 36, Issue. 3-4, p. 535.


    Bárány, I. 1995. The limit shape of convex lattice polygons. Discrete & Computational Geometry, Vol. 13, Issue. 3-4, p. 279.


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  • Combinatorics, Probability and Computing, Volume 1, Issue 4
  • December 1992, pp. 295-302

On the Number of Convex Lattice Polygons

  • Imre Bárány (a1) and János Pach (a2)
  • DOI: http://dx.doi.org/10.1017/S0963548300000341
  • Published online: 01 September 2008
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.

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[2]G. E. Andrews (1965) A lower bound for the volumes of strictly convex bodies with many boundary points. Trans. Amer. Math. Soc. 106 270279.

[5]G. Rademacher (1973) Topics in Analytic Number Theory, Springer.

[7]W. Schmidt (1985) Integer points on curves and surfaces. Monatshefte Math. 99 4582.

[8]G. Szekeres (1951) On the theory of partitions. Quarterly J. Math. Oxford, Second Series 2 85108.

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Combinatorics, Probability and Computing
  • ISSN: 0963-5483
  • EISSN: 1469-2163
  • URL: /core/journals/combinatorics-probability-and-computing
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