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

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.

Authors

Publication Details

Journal
arXiv (Cornell University)
Published
2026-10-29
DOI
https://doi.org/10.48550/arxiv.2610.40095
Primary Topic
Advanced Combinatorial Mathematics
Type
preprint
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preprint

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

Dongchun Han, Hanbin Zhang
arXiv (Cornell University)
Advanced Combinatorial Mathematics
preprint

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

Dongchun Han, Hanbin Zhang
preprint en

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.

arXiv (Cornell University)
Advanced Combinatorial Mathematics
DOIOpen Access PDFOpenAlex
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On the Erdős--Ginzburg--Ziv Problem for $\mathbb{Z}_n^r$ — Dongchun Han, Hanbin Zhang · arXiv (Cornell University) (2026) | TGRS Research Map | TGRS