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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 "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1807.04112","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-11T13:06:38Z","cross_cats_sorted":[],"title_canon_sha256":"09f4c225191a11fadc1d381ea63a9fa45f693e8b9e10a28ca88de9282134ee6c","abstract_canon_sha256":"0d369552e1d323584ba158d208dfcdaf7a71537949a00216cfd2edd15d604f99"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:57.921901Z","signature_b64":"f4+hiLuIukD3bXRTg3YCtyJozqA133KdXAfQZUUlgyZ2yPMSQdTwUq1C4IzlLFQUfgASNWrYSbYaOmtP7xiMDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"61237923e1d468bb8431eca195200083360849be536bd81831f9ed810e13d2db","last_reissued_at":"2026-05-18T00:10:57.921195Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:57.921195Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $\\sum_{j=1}^t a_jx_{i_j}=0$. 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