{"paper":{"title":"The Weighted Davenport Constant of a group and a related extremal problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Eshita Mazumdar, Niranjan Balachandran","submitted_at":"2018-07-11T13:06:38Z","abstract_excerpt":"For a finite abelian group $G$ written additively, and a non-empty subset $A\\subset [1,\\exp(G)-1]$ the weighted Davenport Constant of $G$ with respect to the set $A$, denoted $D_A(G)$, is the least positive integer $k$ for which the following holds: Given an arbitrary $G$-sequence $(x_1,\\ldots,x_k)$, there exists a non-empty subsequence $(x_{i_1},\\ldots,x_{i_t})$ along with $a_{j}\\in A$ such that $\\sum_{j=1}^t a_jx_{i_j}=0$. In this paper, we pose and study a natural new extremal problem that arises from the study of $D_A(G)$: For an integer $k\\ge 2$, determine $\\fD_G(k):=\\min\\{|A|: D_A(G)\\le "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.04112","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"}