{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:WEA6ZO2TH4T44X5IOIVEVVHMR6","short_pith_number":"pith:WEA6ZO2T","schema_version":"1.0","canonical_sha256":"b101ecbb533f27ce5fa8722a4ad4ec8fabab0f02e5f37356351c3473970f1939","source":{"kind":"arxiv","id":"1907.11236","version":1},"attestation_state":"computed","paper":{"title":"Modified Erd\\H{o}s-Ginzburg-Ziv Constants for $(\\mathbb{Z}/n\\mathbb{Z})^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Trajan Hammonds","submitted_at":"2019-07-25T21:12:21Z","abstract_excerpt":"For an abelian group $G$ and an integer $t > 0$, the modified Erd\\H{o}s-Ginzburg-Ziv constant $s'_t(G)$ is the smallest integer $\\ell$ such that any zero-sum sequence of length at least $\\ell$ with elements in $G$ contains a zero-sum subsequence (not necessarily consecutive) of length $t$. We compute bounds for $s'_{t}(G)$ for $G = \\left(\\mathbb{Z}/n\\mathbb{Z}\\right)^2$ and $G = \\left(\\mathbb{Z}/n_1\\mathbb{Z} \\times \\mathbb{Z}/n_2\\mathbb{Z}\\right)$. We also compute bounds for $G = \\left(\\mathbb{Z}/p\\mathbb{Z}\\right)^d$ where the subsequence can be any length in $\\{p, \\dots, (d-1)p\\}$. Lastly, "},"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":"1907.11236","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-07-25T21:12:21Z","cross_cats_sorted":[],"title_canon_sha256":"47b55a3487293206b8bdadafff61c1e00833e1184a7ac1f713b0dfb4634ecf4e","abstract_canon_sha256":"c41a042a7c0b1683be592a80493fc8fb49d627bbb85057668457ca09fbd4dfe9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:29.731969Z","signature_b64":"nYJ8r3CFJBLEvcc7cGVCXQyciJp71MoDzP7hUItcfubczNCtNJBN28KMPQhKdDNPSymiKMxpbMKbC3UfuxIsCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b101ecbb533f27ce5fa8722a4ad4ec8fabab0f02e5f37356351c3473970f1939","last_reissued_at":"2026-05-17T23:39:29.731455Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:29.731455Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Modified Erd\\H{o}s-Ginzburg-Ziv Constants for $(\\mathbb{Z}/n\\mathbb{Z})^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Trajan Hammonds","submitted_at":"2019-07-25T21:12:21Z","abstract_excerpt":"For an abelian group $G$ and an integer $t > 0$, the modified Erd\\H{o}s-Ginzburg-Ziv constant $s'_t(G)$ is the smallest integer $\\ell$ such that any zero-sum sequence of length at least $\\ell$ with elements in $G$ contains a zero-sum subsequence (not necessarily consecutive) of length $t$. We compute bounds for $s'_{t}(G)$ for $G = \\left(\\mathbb{Z}/n\\mathbb{Z}\\right)^2$ and $G = \\left(\\mathbb{Z}/n_1\\mathbb{Z} \\times \\mathbb{Z}/n_2\\mathbb{Z}\\right)$. We also compute bounds for $G = \\left(\\mathbb{Z}/p\\mathbb{Z}\\right)^d$ where the subsequence can be any length in $\\{p, \\dots, (d-1)p\\}$. 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