{"paper":{"title":"On the Harborth constant of $C_3 \\oplus C_{3n}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Hanane Zerdoum (LAGA), Luz Elimar Marchan (ESPOL), Oscar Ordaz, Philippe Guillot (LAGA), Wolfgang Schmid (LAGA)","submitted_at":"2018-08-02T09:18:56Z","abstract_excerpt":"For a finite abelian group $(G,+, 0)$ the Harborth constant $\\mathsf{g}(G)$ is the smallest integer $k$ such that each squarefree sequence over $G$ of length $k$, equivalently each subset of $G$ of cardinality at least $k$,  has a subsequence of length $\\exp(G)$ whose sum is $0$. In this paper, it is established that  $\\mathsf{g}(G)= 3n + 3$ for prime $n \\neq 3$ and $\\mathsf{g}(C_3 \\oplus C_9)= 13$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.00722","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"}