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It was conjectured by R.B.~Eggleton and P.~Erd\\\"{o}s in 1972 and proved by W.~Gao et. al. in 2008 that $|\\Sigma(S)|\\geq 19$ provided that $S$ is a zero-sum free subset of an abelian group $G$ with $|S|=6$. In this paper, we determined the structure of zero-sum free set $S$ where $|S|=6$ and $|\\Sigma(S)|=19$."},"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":"1801.00131","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-12-30T13:09:55Z","cross_cats_sorted":[],"title_canon_sha256":"c0d685fbbee09be5c589f4bedaeeeb6ead9f50abf518fada93017a79db86d82d","abstract_canon_sha256":"90b1be91b5c5279924bca2b8e356d1453049b4a3b116e4b3d52728ddffe3390a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:59.323658Z","signature_b64":"yhPRxzNyv03coAkD9koHzG6UN9hNuHEB0umm16jqOOy8drMYFZ0SucesfT27WDqwCG1QkesSPkGAWMtU+YqtCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9868aab089b5147b0a15eb2ae06c55d074e394b8e5c9fc20e77b4591a43d04e9","last_reissued_at":"2026-05-18T00:26:59.322978Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:59.322978Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the structure of zero-sum free set with minimum subset sums in abelian groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jiangtao Peng, Wanzhen Hui","submitted_at":"2017-12-30T13:09:55Z","abstract_excerpt":"Let $G$ be an additive abelian group and $S\\subset G$ a subset. 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