{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:ZEAA6EBSPXAAA73YENRDBXIPIX","short_pith_number":"pith:ZEAA6EBS","schema_version":"1.0","canonical_sha256":"c9000f10327dc0007f78236230dd0f45c93a57c43c4eafe7cfbc88f82fe5e462","source":{"kind":"arxiv","id":"1205.6837","version":1},"attestation_state":"computed","paper":{"title":"Multiplicative Bases for the Centres of the Group Algebra and Iwahori-Hecke Algebra of the Symmetric Group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Andrew Francis, Lenny Jones","submitted_at":"2012-05-30T21:21:20Z","abstract_excerpt":"Let $\\H_n$ be the Iwahori-Hecke algebra of the symmetric group $S_n$, and let $Z(\\H_n)$ denote its centre. Let $B={b_1,b_2,...,b_t}$ be a basis for $Z(\\H_n)$ over $R=\\Z[q,q^{-1}]$. Then $B$ is called \\emph{multiplicative} if, for every $i$ and $j$, there exists $k$ such that $b_ib_j= b_k$. In this article we prove that there are no multiplicative bases for $Z(\\Z S_n)$ and $Z(\\H_n)$ when $n\\ge 3$. In addition, we prove that there exist exactly two multiplicative bases for $Z(\\Z S_2)$ and none for $Z(\\H_2)$."},"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":"1205.6837","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-05-30T21:21:20Z","cross_cats_sorted":[],"title_canon_sha256":"8b61696fb1baf3735a6fc627e185a9f922c66e093de21776ce7bcdb799a2d674","abstract_canon_sha256":"d27dd23dc298ac3675441420149d744b66cd656a2edfe056ffb57ef43b5095fc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:54:36.772911Z","signature_b64":"DLYmFFw9pLYiBCOESizQA1DgAaYn01ObSphJy/7JPwT022Dx56LCXfbAH/umFMeooAxnxqovzxthXLOeQU08AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c9000f10327dc0007f78236230dd0f45c93a57c43c4eafe7cfbc88f82fe5e462","last_reissued_at":"2026-05-18T03:54:36.772399Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:54:36.772399Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Multiplicative Bases for the Centres of the Group Algebra and Iwahori-Hecke Algebra of the Symmetric Group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Andrew Francis, Lenny Jones","submitted_at":"2012-05-30T21:21:20Z","abstract_excerpt":"Let $\\H_n$ be the Iwahori-Hecke algebra of the symmetric group $S_n$, and let $Z(\\H_n)$ denote its centre. Let $B={b_1,b_2,...,b_t}$ be a basis for $Z(\\H_n)$ over $R=\\Z[q,q^{-1}]$. Then $B$ is called \\emph{multiplicative} if, for every $i$ and $j$, there exists $k$ such that $b_ib_j= b_k$. In this article we prove that there are no multiplicative bases for $Z(\\Z S_n)$ and $Z(\\H_n)$ when $n\\ge 3$. In addition, we prove that there exist exactly two multiplicative bases for $Z(\\Z S_2)$ and none for $Z(\\H_2)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6837","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":"1205.6837","created_at":"2026-05-18T03:54:36.772487+00:00"},{"alias_kind":"arxiv_version","alias_value":"1205.6837v1","created_at":"2026-05-18T03:54:36.772487+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.6837","created_at":"2026-05-18T03:54:36.772487+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZEAA6EBSPXAA","created_at":"2026-05-18T12:27:30.460161+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZEAA6EBSPXAAA73Y","created_at":"2026-05-18T12:27:30.460161+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZEAA6EBS","created_at":"2026-05-18T12:27:30.460161+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/ZEAA6EBSPXAAA73YENRDBXIPIX","json":"https://pith.science/pith/ZEAA6EBSPXAAA73YENRDBXIPIX.json","graph_json":"https://pith.science/api/pith-number/ZEAA6EBSPXAAA73YENRDBXIPIX/graph.json","events_json":"https://pith.science/api/pith-number/ZEAA6EBSPXAAA73YENRDBXIPIX/events.json","paper":"https://pith.science/paper/ZEAA6EBS"},"agent_actions":{"view_html":"https://pith.science/pith/ZEAA6EBSPXAAA73YENRDBXIPIX","download_json":"https://pith.science/pith/ZEAA6EBSPXAAA73YENRDBXIPIX.json","view_paper":"https://pith.science/paper/ZEAA6EBS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1205.6837&json=true","fetch_graph":"https://pith.science/api/pith-number/ZEAA6EBSPXAAA73YENRDBXIPIX/graph.json","fetch_events":"https://pith.science/api/pith-number/ZEAA6EBSPXAAA73YENRDBXIPIX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZEAA6EBSPXAAA73YENRDBXIPIX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZEAA6EBSPXAAA73YENRDBXIPIX/action/storage_attestation","attest_author":"https://pith.science/pith/ZEAA6EBSPXAAA73YENRDBXIPIX/action/author_attestation","sign_citation":"https://pith.science/pith/ZEAA6EBSPXAAA73YENRDBXIPIX/action/citation_signature","submit_replication":"https://pith.science/pith/ZEAA6EBSPXAAA73YENRDBXIPIX/action/replication_record"}},"created_at":"2026-05-18T03:54:36.772487+00:00","updated_at":"2026-05-18T03:54:36.772487+00:00"}