{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2001:SF354H4COS34LZVKX4AZZ2CDSJ","short_pith_number":"pith:SF354H4C","schema_version":"1.0","canonical_sha256":"9177de1f8274b7c5e6aabf019ce843925d51d36c8a9972a2c3bafc20c1b55d5b","source":{"kind":"arxiv","id":"math/0201003","version":3},"attestation_state":"computed","paper":{"title":"Rim Hook Tableaux and Kostant's $\\eta$-Function Coefficients","license":"","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CO","authors_text":"Avital Frumkin, Ron M. Adin","submitted_at":"2001-12-31T23:29:00Z","abstract_excerpt":"Using a 0/1 encoding of Young diagrams and its consequences for rim hook tableaux, we prove a reduction formula of Littlewood for arbitrary characters of the symmetric group, evaluated at elements with all cycle lengths divisible by a given integer. As an application, we find explicitly the coefficients in a formula of Kostant for certain powers of the Dedekind $\\eta$-function, avoiding most of the original machinery."},"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":"math/0201003","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.CO","submitted_at":"2001-12-31T23:29:00Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"ef913119764bfe929ce57223be67863e492271b7020f45cd9019bd18ec4648ea","abstract_canon_sha256":"70c1e98c575864d869020e828de05a5a1361b8ec382f6e5de38058f0aaf672d6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:35:50.567288Z","signature_b64":"3bzkAJg5bU6AJnOLlnfntCX4SxSCG2+CR9WqTlWCg7YOgvZXdD0X5kWoHeGYOQ8IiY1zsA+R/j8J8s/CELduAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9177de1f8274b7c5e6aabf019ce843925d51d36c8a9972a2c3bafc20c1b55d5b","last_reissued_at":"2026-07-04T14:35:50.566912Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:35:50.566912Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rim Hook Tableaux and Kostant's $\\eta$-Function Coefficients","license":"","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CO","authors_text":"Avital Frumkin, Ron M. Adin","submitted_at":"2001-12-31T23:29:00Z","abstract_excerpt":"Using a 0/1 encoding of Young diagrams and its consequences for rim hook tableaux, we prove a reduction formula of Littlewood for arbitrary characters of the symmetric group, evaluated at elements with all cycle lengths divisible by a given integer. As an application, we find explicitly the coefficients in a formula of Kostant for certain powers of the Dedekind $\\eta$-function, avoiding most of the original machinery."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0201003","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0201003/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"math/0201003","created_at":"2026-07-04T14:35:50.566976+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0201003v3","created_at":"2026-07-04T14:35:50.566976+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0201003","created_at":"2026-07-04T14:35:50.566976+00:00"},{"alias_kind":"pith_short_12","alias_value":"SF354H4COS34","created_at":"2026-07-04T14:35:50.566976+00:00"},{"alias_kind":"pith_short_16","alias_value":"SF354H4COS34LZVK","created_at":"2026-07-04T14:35:50.566976+00:00"},{"alias_kind":"pith_short_8","alias_value":"SF354H4C","created_at":"2026-07-04T14:35:50.566976+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2409.01005","citing_title":"On Hecke and asymptotic categories for a family of complex reflection groups","ref_index":1,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/SF354H4COS34LZVKX4AZZ2CDSJ","json":"https://pith.science/pith/SF354H4COS34LZVKX4AZZ2CDSJ.json","graph_json":"https://pith.science/api/pith-number/SF354H4COS34LZVKX4AZZ2CDSJ/graph.json","events_json":"https://pith.science/api/pith-number/SF354H4COS34LZVKX4AZZ2CDSJ/events.json","paper":"https://pith.science/paper/SF354H4C"},"agent_actions":{"view_html":"https://pith.science/pith/SF354H4COS34LZVKX4AZZ2CDSJ","download_json":"https://pith.science/pith/SF354H4COS34LZVKX4AZZ2CDSJ.json","view_paper":"https://pith.science/paper/SF354H4C","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0201003&json=true","fetch_graph":"https://pith.science/api/pith-number/SF354H4COS34LZVKX4AZZ2CDSJ/graph.json","fetch_events":"https://pith.science/api/pith-number/SF354H4COS34LZVKX4AZZ2CDSJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SF354H4COS34LZVKX4AZZ2CDSJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SF354H4COS34LZVKX4AZZ2CDSJ/action/storage_attestation","attest_author":"https://pith.science/pith/SF354H4COS34LZVKX4AZZ2CDSJ/action/author_attestation","sign_citation":"https://pith.science/pith/SF354H4COS34LZVKX4AZZ2CDSJ/action/citation_signature","submit_replication":"https://pith.science/pith/SF354H4COS34LZVKX4AZZ2CDSJ/action/replication_record"}},"created_at":"2026-07-04T14:35:50.566976+00:00","updated_at":"2026-07-04T14:35:50.566976+00:00"}