{"paper":{"title":"Remarks on a generalization of the Davenport constant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.CO"],"primary_cat":"math.NT","authors_text":"Michael Freeze, Wolfgang A. Schmid","submitted_at":"2009-05-26T17:27:45Z","abstract_excerpt":"A generalization of the Davenport constant is investigated. For a finite abelian group $G$ and a positive integer $k$, let $D_k(G)$ denote the smallest $\\ell$ such that each sequence over $G$ of length at least $\\ell$ has $k$ disjoint non-empty zero-sum subsequences. For general $G$, expanding on known results, upper and lower bounds on these invariants are investigated and it is proved that the sequence $(D_k(G))_{k\\in\\mathbb{N}}$ is eventually an arithmetic progression with difference $\\exp(G)$, and several questions arising from this fact are investigated. For elementary 2-groups, $D_k(G)$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.4248","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"}