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Let $\\mathcal{S}_R$ be the multiplicative semigroup of the ring $R$, and let ${\\rm U}(\\mathcal{S}_R)$ be the group of units of $\\mathcal{S}_R$. The Davenport constant ${\\rm D}(\\mathcal{S}_R)$ of the multiplicative semigroup $\\mathcal{S}_R$ is the least positive integer $\\ell$ such that for any $\\ell$ polynomials $g_1,g_2,\\ldots,g_{\\ell}\\in \\F_q[x]$, there exists a subset $I\\subsetneq [1,\\ell]$ wi"},"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":"1507.03182","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-07-12T03:37:19Z","cross_cats_sorted":["math.AC","math.NT"],"title_canon_sha256":"3b185f981c8dcff482a2ff63c5aebe55faabf3e62c328d8a5536f2ffa0cbbac6","abstract_canon_sha256":"4b64c039c10c1321a124a0ac6b68279467f9217310642f028e68ceb5a6dad739"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:59.472542Z","signature_b64":"LGFZQga1yeibT/rQZVjEMoEOHLODtTgdkG3bbo3hqMHuRbzem9WnGU/NqHEOPTD4qdc095BL4cR4b9vN4hTeBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eefa225adec352797b801837771fcd643fa658662f2f0b972a75493674f0e4e8","last_reissued_at":"2026-05-18T01:36:59.471798Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:59.471798Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A problem of Wang on Davenport constant for the multiplicative semigroup of the quotient ring of $\\F_2[x]$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.NT"],"primary_cat":"math.CO","authors_text":"Haoli Wang, Lizhen Zhang, Yongke Qu","submitted_at":"2015-07-12T03:37:19Z","abstract_excerpt":"Let $\\F_q[x]$ be the ring of polynomials over the finite field $\\F_q$, and let $f$ be a polynomial of $\\F_q[x]$. Let $R=\\frac{\\F_q[x]}{(f)}$ be a quotient ring of $\\F_q[x]$ with $0\\neq R\\neq \\F_q[x]$. Let $\\mathcal{S}_R$ be the multiplicative semigroup of the ring $R$, and let ${\\rm U}(\\mathcal{S}_R)$ be the group of units of $\\mathcal{S}_R$. The Davenport constant ${\\rm D}(\\mathcal{S}_R)$ of the multiplicative semigroup $\\mathcal{S}_R$ is the least positive integer $\\ell$ such that for any $\\ell$ polynomials $g_1,g_2,\\ldots,g_{\\ell}\\in \\F_q[x]$, there exists a subset $I\\subsetneq [1,\\ell]$ wi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.03182","kind":"arxiv","version":1},"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":"1507.03182","created_at":"2026-05-18T01:36:59.471905+00:00"},{"alias_kind":"arxiv_version","alias_value":"1507.03182v1","created_at":"2026-05-18T01:36:59.471905+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.03182","created_at":"2026-05-18T01:36:59.471905+00:00"},{"alias_kind":"pith_short_12","alias_value":"535CEWW6YNJH","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_16","alias_value":"535CEWW6YNJHS64A","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_8","alias_value":"535CEWW6","created_at":"2026-05-18T12:29:05.191682+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/535CEWW6YNJHS64ADA3XOH6NMQ","json":"https://pith.science/pith/535CEWW6YNJHS64ADA3XOH6NMQ.json","graph_json":"https://pith.science/api/pith-number/535CEWW6YNJHS64ADA3XOH6NMQ/graph.json","events_json":"https://pith.science/api/pith-number/535CEWW6YNJHS64ADA3XOH6NMQ/events.json","paper":"https://pith.science/paper/535CEWW6"},"agent_actions":{"view_html":"https://pith.science/pith/535CEWW6YNJHS64ADA3XOH6NMQ","download_json":"https://pith.science/pith/535CEWW6YNJHS64ADA3XOH6NMQ.json","view_paper":"https://pith.science/paper/535CEWW6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1507.03182&json=true","fetch_graph":"https://pith.science/api/pith-number/535CEWW6YNJHS64ADA3XOH6NMQ/graph.json","fetch_events":"https://pith.science/api/pith-number/535CEWW6YNJHS64ADA3XOH6NMQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/535CEWW6YNJHS64ADA3XOH6NMQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/535CEWW6YNJHS64ADA3XOH6NMQ/action/storage_attestation","attest_author":"https://pith.science/pith/535CEWW6YNJHS64ADA3XOH6NMQ/action/author_attestation","sign_citation":"https://pith.science/pith/535CEWW6YNJHS64ADA3XOH6NMQ/action/citation_signature","submit_replication":"https://pith.science/pith/535CEWW6YNJHS64ADA3XOH6NMQ/action/replication_record"}},"created_at":"2026-05-18T01:36:59.471905+00:00","updated_at":"2026-05-18T01:36:59.471905+00:00"}