Given an additively written abelian group G and a set X ⊆ G, we let (X) denote the monoid of zero-sum sequences over X and (X) the Davenport constant of (X), namely the supremum of the positive integers n for which there exists a sequence x₁⋯xₙ in (X) such that for each non-empty proper subset I of 1,...,n. In this paper, we mainly investigate the case when G is a power of ℤ and X is a box (i.e., a product of intervals of G). Some mixed sets (e.g., the product of a group by a box) are studied too, and some inverse results are obtained.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa171-3-1,
author = {Alain Plagne},
title = {The Davenport constant of a box},
journal = {Acta Arithmetica},
volume = {168},
year = {2015},
pages = {197-219},
zbl = {06498807},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa171-3-1}
}
Alain Plagne. The Davenport constant of a box. Acta Arithmetica, Tome 168 (2015) pp. 197-219. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa171-3-1/