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On the Erdős--Ginzburg--Ziv Problem for ℤnr
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 4r n lattice points in ℤr contains n points whose centroid is again a lattice point.
Related
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BibTeX
@misc{han2026erdősginzburgziv,
title = {{On the Erdős--Ginzburg--Ziv Problem for $\mathbbZ_n^r$}},
author = {Dongchun Han and Hanbin Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.40095},
eprint = {2610.40095},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.40095},
}
RIS
TY - UNPB
TI - On the Erdős--Ginzburg--Ziv Problem for ℤ_n^r
AU - Dongchun Han
AU - Hanbin Zhang
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.40095
UR - https://arxiv.org/abs/2610.40095
AB - 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 ℤ^r contains n points whose centroid is again a lattice point.
ER -