On the Erdős--Ginzburg--Ziv Problem for $\mathbb{Z}_n^r$

Dongchun Han; Hanbin Zhang

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arXiv · 2610.40095

On the Erdős--Ginzburg--Ziv Problem for $\mathbb{Z}_n^r$

Dongchun Han·Hanbin Zhang

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Abstract

The Erdős--Ginzburg--Ziv problem is a classical extremal problem in discrete geometry. We prove that, for all positive integers $n$ and $r$, every sequence of $4^r n$ lattice points in $\mathbb{Z}^r$ contains $n$ points whose centroid is again a lattice point.

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Dongchun Han, Hanbin Zhang. 2026-10-29. On the Erdős--Ginzburg--Ziv Problem for $\mathbb{Z}_n^r$. https://arxiv.org/abs/2610.40095

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