PreprintCC BY 4.0HAL
The Davenport constant of balls and boxes
Abstract
Given an additively written abelian group G and a set X⊆ G, we let D(X) denote the Davenport constant of X, namely the largest non-negative integer n for which there exists a sequence x1, …, xn of elements of X such that ∑i=1n xi =0 and ∑i ∈ I xi ≠ 0 for each non-empty proper subset I of {1, …, n}. In this paper, we mainly investigate the case when G is ℤ2 and ℤ3, and X is a discrete Euclidean ball. An application to the classical problem of estimating the Davenport constant of a box - a product of intervals of integers - is then obtained.
Related
BibTeX
@misc{girard2026davenport,
title = {{The Davenport constant of balls and boxes}},
author = {Benjamin Girard and Alain Plagne},
howpublished = {HAL},
year = {2026},
month = oct,
url = {https://hal.science/hal-05328809v2},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Davenport constant of balls and boxes
AU - Benjamin Girard
AU - Alain Plagne
PY - 2026
DA - 2026/10/08
PB - HAL
UR - https://hal.science/hal-05328809v2
AB - Given an additively written abelian group G and a set X⊆ G, we let D(X) denote the Davenport constant of X, namely the largest non-negative integer n for which there exists a sequence x_1, …, x_n of elements of X such that ∑_i=1^n x_i =0 and ∑_i ∈ I x_i ≠ 0 for each non-empty proper subset I of {1, …, n}. In this paper, we mainly investigate the case when G is ℤ^2 and ℤ^3, and X is a discrete Euclidean ball. An application to the classical problem of estimating the Davenport constant of a box - a product of intervals of integers - is then obtained.
ER -