The Davenport constant of a box

Alain Plagne. "The Davenport constant of a box." Acta Arithmetica 171.3 (2015): 197-219. <http://eudml.org/doc/279844>.

@article{AlainPlagne2015,
abstract = {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 $∑_\{i ∈ I\} x_i ≠ 0$ for each non-empty proper subset I of 1,...,n. In this paper, we mainly investigate the case when G is 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.},
author = {Alain Plagne},
journal = {Acta Arithmetica},
keywords = {additive combinatorics; Davenport constant; inverse theorem; minimal zero-sum sequence},
language = {eng},
number = {3},
pages = {197-219},
title = {The Davenport constant of a box},
url = {http://eudml.org/doc/279844},
volume = {171},
year = {2015},
}

TY - JOUR
AU - Alain Plagne
TI - The Davenport constant of a box
JO - Acta Arithmetica
PY - 2015
VL - 171
IS - 3
SP - 197
EP - 219
AB - 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 $∑_{i ∈ I} x_i ≠ 0$ for each non-empty proper subset I of 1,...,n. In this paper, we mainly investigate the case when G is 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.
LA - eng
KW - additive combinatorics; Davenport constant; inverse theorem; minimal zero-sum sequence
UR - http://eudml.org/doc/279844
ER -