{"paper":{"title":"On the lower bounds of Davenport constant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Chao Liu","submitted_at":"2018-10-19T03:30:49Z","abstract_excerpt":"Let $G = C_{n_1} \\oplus \\cdots \\oplus C_{n_r}$ with $1 < n_1 | \\cdots | n_r$ be a finite abelian group. The Davenport constant $\\mathsf D(G)$ is the smallest integer $t$ such that every sequence $S$ over $G$ of length $|S|\\ge t$ has a non-empty zero-sum subsequence. It is a starting point of zero-sum theory but only has a trivial lower bound $\\mathsf D^*(G) = n_1 + \\cdots + n_r - r + 1$, which equals $\\mathsf D(G)$ over $p$-groups. We investigate the non-dispersive sequences over group $C_n^r$, thereby revealing the growth of $\\mathsf D(G)-\\mathsf D^*(G)$ over non-$p$-groups $G = C_n^r \\oplus "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.08346","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1810.08346/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}