{"paper":{"title":"The Davenport constant of a box","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Alain Plagne, Salvatore Tringali","submitted_at":"2014-05-17T07:18:47Z","abstract_excerpt":"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 $x_1 \\cdots x_n$ of $\\mathscr{B}(X)$ 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 o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.4363","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}