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The Davenport constant of a box

Volume 171 / 2015

Alain Plagne, Salvatore Tringali Acta Arithmetica 171 (2015), 197-219 MSC: Primary 11B75; Secondary 11B30, 11P70. DOI: 10.4064/aa171-3-1


Given an additively written abelian group $G$ 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.


  • Alain PlagneCentre de math\'ematiques Laurent Schwartz
    \'Ecole polytechnique
    91128 Palaiseau Cedex, France
  • Salvatore TringaliScience Program
    Texas A\&M University at Qatar
    Education City
    PO Box 23874, Doha, Qatar

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