On Kemnitz' Conjecture Concerning Lattice Points in the Plane

Abstract

In 1961, P. Erdős, A. Ginzburg, and A. 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.

Cited by in corpus (4)

• Inverse zero-sum problems for certain groups of rank three
• Zero-sum Subsequences of Length kq over Finite Abelian p-Groups
• On generalized Erdős-Ginzburg-Ziv constants for ${\mathbb{Z}}_2^d$
• Extremal problems on the hypercube and the codegree Turán density of complete $r$-graphs