Advertisement

The Ramanujan Journal

, Volume 13, Issue 1–3, pp 333–337 | Cite as

On Kemnitz’ conjecture concerning lattice-points in the plane

  • Christian Reiher
Article

Abstract

In 1961, Erdős, Ginzburg and Ziv proved a remarkable theorem stating that each set of 2n−1 integers contains a subset of size n, the sum of whose elements is divisible by n. We will prove a similar result for pairs of integers, i.e. planar lattice-points, usually referred to as Kemnitz’ conjecture.

Keywords

Zero-sum-subsets Kemnitz’ Conjecture 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Alon, N., Dubiner, D.: A lattice point problem and additive number theory. Combinatorica 15, 301–309 (1995)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Erdős, P., Ginzburg, A., Ziv, A.: Theorem in the additive number theory. Bull Research Council Israel 10F, 41–43 (1961)Google Scholar
  3. 3.
    Gao, W.: Note on a zero-sum problem. J. Combin. Theory, Series A 95, 387–389 (2001)CrossRefGoogle Scholar
  4. 4.
    Kemnitz, A.: On a lattice point problem. Ars Combin. 16b, 151–160 (1983)MathSciNetGoogle Scholar
  5. 5.
    Rónyai, L.: On a conjecture of Kemnitz. Combinatorica 20, 569–573 (2000)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Schmidt, W.M.: Equations Over Finite Fields, An Elementary Approach. Springer Verlag, Lecture Notes in Math (1976)Google Scholar

Copyright information

© Springer Science + Business Media, LLC 2006

Authors and Affiliations

  1. 1.Oxford UniversityUK

Personalised recommendations