{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:QHQPPF37QQXAACKAXJISHFSHOH","short_pith_number":"pith:QHQPPF37","schema_version":"1.0","canonical_sha256":"81e0f7977f842e000940ba5123964771de0c9cede136d21893ef81e09c18f1c9","source":{"kind":"arxiv","id":"1409.2077","version":3},"attestation_state":"computed","paper":{"title":"Davenport constant for semigroups II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.NT"],"primary_cat":"math.CO","authors_text":"Guoqing Wang","submitted_at":"2014-09-07T03:08:07Z","abstract_excerpt":"Let $\\mathcal{S}$ be a finite commutative semigroup. The Davenport constant of $\\mathcal{S}$, denoted ${\\rm D}(\\mathcal{S})$, is defined to be the least positive integer $\\ell$ such that every sequence $T$ of elements in $\\mathcal{S}$ of length at least $\\ell$ contains a proper subsequence $T'$ ($T'\\neq T$) with the sum of all terms from $T'$ equaling the sum of all terms from $T$. Let $q>2$ be a prime power, and let $\\F_q[x]$ be the ring of polynomials over the finite field $\\F_q$. Let $R$ be a quotient ring of $\\F_q[x]$ with $0\\neq R\\neq \\F_q[x]$. We prove that $${\\rm D}(\\mathcal{S}_R)={\\rm "},"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":"1409.2077","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-09-07T03:08:07Z","cross_cats_sorted":["math.GR","math.NT"],"title_canon_sha256":"7277afbcc405aa9cfd1cc3a8da50063725ae7767097ec8911f47b3065415e5e6","abstract_canon_sha256":"ec9ba476d38143b0e0a3b1f891d7fc10392b16e98e813dce2c85fc7bff8b5bbe"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:19.821472Z","signature_b64":"ca9z64pvi0h5q7UHp8FfZ59+QwB+ApP7ZqVsoCpHQXWTZ0AbNsIe+ugdFmGXQm60uNs/gbNPG0svk+YVNWMhCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"81e0f7977f842e000940ba5123964771de0c9cede136d21893ef81e09c18f1c9","last_reissued_at":"2026-05-18T02:25:19.821084Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:19.821084Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Davenport constant for semigroups II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.NT"],"primary_cat":"math.CO","authors_text":"Guoqing Wang","submitted_at":"2014-09-07T03:08:07Z","abstract_excerpt":"Let $\\mathcal{S}$ be a finite commutative semigroup. The Davenport constant of $\\mathcal{S}$, denoted ${\\rm D}(\\mathcal{S})$, is defined to be the least positive integer $\\ell$ such that every sequence $T$ of elements in $\\mathcal{S}$ of length at least $\\ell$ contains a proper subsequence $T'$ ($T'\\neq T$) with the sum of all terms from $T'$ equaling the sum of all terms from $T$. Let $q>2$ be a prime power, and let $\\F_q[x]$ be the ring of polynomials over the finite field $\\F_q$. Let $R$ be a quotient ring of $\\F_q[x]$ with $0\\neq R\\neq \\F_q[x]$. We prove that $${\\rm D}(\\mathcal{S}_R)={\\rm "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.2077","kind":"arxiv","version":3},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1409.2077","created_at":"2026-05-18T02:25:19.821149+00:00"},{"alias_kind":"arxiv_version","alias_value":"1409.2077v3","created_at":"2026-05-18T02:25:19.821149+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.2077","created_at":"2026-05-18T02:25:19.821149+00:00"},{"alias_kind":"pith_short_12","alias_value":"QHQPPF37QQXA","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_16","alias_value":"QHQPPF37QQXAACKA","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_8","alias_value":"QHQPPF37","created_at":"2026-05-18T12:28:46.137349+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QHQPPF37QQXAACKAXJISHFSHOH","json":"https://pith.science/pith/QHQPPF37QQXAACKAXJISHFSHOH.json","graph_json":"https://pith.science/api/pith-number/QHQPPF37QQXAACKAXJISHFSHOH/graph.json","events_json":"https://pith.science/api/pith-number/QHQPPF37QQXAACKAXJISHFSHOH/events.json","paper":"https://pith.science/paper/QHQPPF37"},"agent_actions":{"view_html":"https://pith.science/pith/QHQPPF37QQXAACKAXJISHFSHOH","download_json":"https://pith.science/pith/QHQPPF37QQXAACKAXJISHFSHOH.json","view_paper":"https://pith.science/paper/QHQPPF37","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1409.2077&json=true","fetch_graph":"https://pith.science/api/pith-number/QHQPPF37QQXAACKAXJISHFSHOH/graph.json","fetch_events":"https://pith.science/api/pith-number/QHQPPF37QQXAACKAXJISHFSHOH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QHQPPF37QQXAACKAXJISHFSHOH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QHQPPF37QQXAACKAXJISHFSHOH/action/storage_attestation","attest_author":"https://pith.science/pith/QHQPPF37QQXAACKAXJISHFSHOH/action/author_attestation","sign_citation":"https://pith.science/pith/QHQPPF37QQXAACKAXJISHFSHOH/action/citation_signature","submit_replication":"https://pith.science/pith/QHQPPF37QQXAACKAXJISHFSHOH/action/replication_record"}},"created_at":"2026-05-18T02:25:19.821149+00:00","updated_at":"2026-05-18T02:25:19.821149+00:00"}