Skip to main content
Log in

The limit shape of convex lattice polygons and related topics

  • Published:
Functional Analysis and Its Applications Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. V. I. Arnol'd, “The statistics of convex lattice polygons,” Funkts. Anal. Prilozhen.,14, No 1, 1–3 (1980).

    Google Scholar 

  2. G. E. Andrews, “A lower bound for the volume of strictly convex bodies with many boundary points,” Trans. Am. Math. Soc.,106, 270–279 (1963).

    Google Scholar 

  3. I. Bárány and A. M. Vershik, “On the number of convex lattice polytopes,” Geometric Funct. Anal.,2, No. 4, 381–393 (1992).

    Google Scholar 

  4. A. M. Vershik and S. V. Kerov, “The asymptotic behavior of the maximal and the typical dimension for irreducible representations of the symmetric group,” Funkts. Anal. Prilozhen.,19, 1, 27–36 (1985).

    Google Scholar 

  5. Ya. G. Sinai, “The probabilistic approach to the analysis of statistics for convex polygonal lines,” to appear in Funkts. Anal. Prilozhen.,28, 2 (1994).

    Google Scholar 

  6. V. Jarnik, “Über die Gitterpunkte auf konvexen Curven,” Math. Z.,24, 500–518 (1926).

    Google Scholar 

  7. E. Bombieri and J. Pila, “The number of integral points on arcs and ovals,” Duke. Math. J.,59, No. 2, 337–357 (1989).

    Google Scholar 

  8. W. Schmidt, “Integer points on curves and surfaces,” Monatsh. Math.,99, No. 1, 45–72 (1985).

    Google Scholar 

  9. G. E. Andrews, Number Theory: The Theory of Partitions, Addison-Wesley (1976).

  10. E. Wright, “The number of partitions of a large bi-partite number,” Proc. London Math. Soc.,7, No. 5, 150–160 (1957).

    Google Scholar 

  11. G. Meinardus, “Zur additiven Zahlentheorie in mehreren Dimensionen,” Math. Ann.,132, 333–346 (1956).

    Google Scholar 

  12. W. Blaschke, Affine Differentialgeometrie, Berlin (1923).

  13. P. A. Shirokov and A. P. Shirokov, Affine Differential Geometry [in Russian], Fizmatgiz, Moscow (1959).

    Google Scholar 

  14. I. Bárány and D. G. Larman, “Convex bodies, economic cap coverings, random polytopes,” Mathematika,35, 274–291 (1988).

    Google Scholar 

  15. P. V. Sporyshev and A. M. Vershik, “Asymptotic behavior of the number of faces of random polyhedra and the neighborliness problem,” Selecta Math. Soviet.,12, No. 1 (1992).

    Google Scholar 

  16. R. Dobrushin, R. Kotecky, and S. Shlosman, Wulff Construction, a Global Shape from Local Interaction, AMS Mathematical Monographs, Vol. 104 (1992).

  17. I. Bárány, “The limit shape theorem for convex lattice polygons,” to appear.

Download references

Authors

Additional information

St. Petersburg Division of the Mathematical Institute of the Russian Academy of Sciences. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 28, No. 1, pp. 16–25, January–March, 1994.

To I. M. Gel'fand on his 80th birthday

Rights and permissions

Reprints and permissions

About this article

Cite this article

Vershik, A.M. The limit shape of convex lattice polygons and related topics. Funct Anal Its Appl 28, 13–20 (1994). https://doi.org/10.1007/BF01079006

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01079006

Keywords

Navigation