{"paper":{"title":"On the Davenport constant and on the structure of extremal zero-sum free sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Alfred Geroldinger, Andreas Philipp, Manfred Liebmann","submitted_at":"2010-09-29T10:43:06Z","abstract_excerpt":"Let $G = C_{n_1} \\oplus ... \\oplus C_{n_r}$ with $1 < n_1 \\t ... \\t n_r$ be a finite abelian group, $\\mathsf d^* (G) = n_1 + ... + n_r - r$, and let $\\mathsf d (G)$ denote the maximal length of a zero-sum free sequence over $G$. Then $\\mathsf d (G) \\ge \\mathsf d^* (G)$, and the standing conjecture is that equality holds for $G = C_n^r$. We show that equality does not hold for $C_2 \\oplus C_{2n}^r$, where $n \\ge 3$ is odd and $r \\ge 4$. This gives new information on the structure of extremal zero-sum free sequences over $C_{2n}^r$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.5835","kind":"arxiv","version":1},"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"}