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Every sequence $S$ of length $l$ over $G$ can be written in the form $S=(n_1g)\\cdot\\ldots\\cdot(n_lg)$ where $g\\in G$ and $n_1, \\ldots, n_l\\in[1, \\ord(g)]$, and the index $\\ind(S)$ of $S$ is defined to be the minimum of $(n_1+\\cdots+n_l)/\\ord(g)$ over all possible $g\\in G$ such that $\\langle g \\rangle =G$. In this paper, we determine the index of any minimal zero-sum sequence $S$ of length 5 when $G=\\langle g\\rangle$ is a cyclic group of a prime order and $S$ has the form $S=g^2(n_2g)(n_3g)(n_4g)$. It is shown that if $G=\\langle g\\rangle$ is a cyclic group of p"},"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":"1303.1676","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-03-07T13:15:20Z","cross_cats_sorted":[],"title_canon_sha256":"7e3d35a016113f9cf623e140671c5bf730b19d506c748fca4abb341b457554d3","abstract_canon_sha256":"475584536e6c1b56a55b0516450680b9dbc5bc954924b3443f201ad837290207"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:31:33.441428Z","signature_b64":"9E11alkM0mNZhOlYpywPGKki71OdNNsHTKoKGvtNXaUaVbmMQM7uDuRopbR9wNIutCDz82RJzE6ErG7bBmCmDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c2c74bb317b0339890bea0b82120b7d645be1e36ef95fc42115e3dcd1d5a61d8","last_reissued_at":"2026-05-18T03:31:33.440748Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:31:33.440748Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Minimal zero-sum sequences of length five over finite cyclic groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jiangtao Peng, Yuanlin Li","submitted_at":"2013-03-07T13:15:20Z","abstract_excerpt":"Let $G$ be a finite cyclic group. Every sequence $S$ of length $l$ over $G$ can be written in the form $S=(n_1g)\\cdot\\ldots\\cdot(n_lg)$ where $g\\in G$ and $n_1, \\ldots, n_l\\in[1, \\ord(g)]$, and the index $\\ind(S)$ of $S$ is defined to be the minimum of $(n_1+\\cdots+n_l)/\\ord(g)$ over all possible $g\\in G$ such that $\\langle g \\rangle =G$. In this paper, we determine the index of any minimal zero-sum sequence $S$ of length 5 when $G=\\langle g\\rangle$ is a cyclic group of a prime order and $S$ has the form $S=g^2(n_2g)(n_3g)(n_4g)$. 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