The Davenport constant of a box
Tom 171 / 2015
Acta Arithmetica 171 (2015), 197-219
MSC: Primary 11B75; Secondary 11B30, 11P70.
DOI: 10.4064/aa171-3-1
Streszczenie
Given an additively written abelian group and a set X\subseteq G, we let \mathscr{B}(X) denote the monoid of zero-sum sequences over X and \mathsf{D}(X) the Davenport constant of \mathscr{B}(X), namely the supremum of the positive integers n for which there exists a sequence x_1 \cdots x_n in \mathscr{B}(X) such that \sum_{i \in I} x_i \ne 0 for each non-empty proper subset I of \{1, \ldots, n\}. In this paper, we mainly investigate the case when G is a power of \mathbb{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.
