Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2025-01-03T19:02:54.461Z Has data issue: false hasContentIssue false
  • English
  • Français

Further inequalities for convex sets with lattice point constraints in the plane

Published online by Cambridge University Press:  17 April 2009

P.R. Scott
P.R. Scott
Affiliation:
Department of Pure Mathematics, University of Adelaide, Adelaide, South Australia 5001, Australia.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let K be a bounded closed convex set in the plane containing no points of the integral lattice in its interior and having width w, area A, perimeter p and circumradius R. The following best possible inequalities are established:

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 21 , Issue 1 , February 1980 , pp. 7 - 12
Copyright
Copyright © Australian Mathematical Society 1980

References

[1]Blaschke, Wilhelm, Kreis und Kugel (Walter de Gruyter, Berlin, 1956).CrossRefGoogle Scholar
[2]Jung, Heinrich, “Ueber die kleinste Kugel, die eine raumliche Figur einschliesst”, J. Reine Angew. Math. 123 (1901), 241–257.Google Scholar
[3]Scott, P.R., “A lattice problem in the plane”, Mathematika 20 (1973), 247–252.CrossRefGoogle Scholar
[4]Scott, P.R., “A family of inequalities for convex sets”, Bull. Austral. Math. Soc. 20 (1979), 237–245.CrossRefGoogle Scholar
[5]Scott, P.R., “Two inequalities for convex sets with lattice point constraints in the plane”, Bull. London Math. Soc. (to appear).Google Scholar