{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2001:KOYZZMVNDMGN5FEFHBDQR2CUDK","short_pith_number":"pith:KOYZZMVN","schema_version":"1.0","canonical_sha256":"53b19cb2ad1b0cde9485384708e8541a8a784044c88b3533488405b2d7a31b10","source":{"kind":"arxiv","id":"math/0105065","version":1},"attestation_state":"computed","paper":{"title":"Noncommutative symmetric functions VI: Free quasi-symmetric functions and related algebras","license":"","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"F. Hivert, G. Duchamp (University of Rouen), J.-Y. Thibon (University of Marne-la-Vallee)","submitted_at":"2001-05-09T10:04:18Z","abstract_excerpt":"This article is devoted to the study of several algebras which are related to symmetric functions, and which admit linear bases labelled by various combinatorial objects: permutations (free quasi-symmetric functions), standard Young tableaux (free symmetric functions) and packed integer matrices (matrix quasi-symmetric functions). Free quasi-symmetric functions provide a kind of noncommutative Frobenius characteristic for a certain category of modules over the 0-Hecke algebras. New examples of indecomposable $H_n(0)$-modules are discussed, and the homological properties of $H_n(0)$ are compute"},"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/0105065","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CO","submitted_at":"2001-05-09T10:04:18Z","cross_cats_sorted":[],"title_canon_sha256":"721fbc1bad2a7c237da403f49c58638f78ec7bc50dab36bd0678649614a0cd13","abstract_canon_sha256":"92b58319899fc9d9db5087b5c5286dc740ac873b5c2873908526c28b57cb8832"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:34:00.591238Z","signature_b64":"PxcXJyTuZtASKhSCI9jZ2FCQWnwTAz/+s9NqSY4muy0TeT14ddnnEF2QQacdZSJF1JvHO8i6bsra9lUOy91HDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"53b19cb2ad1b0cde9485384708e8541a8a784044c88b3533488405b2d7a31b10","last_reissued_at":"2026-05-18T03:34:00.590420Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:34:00.590420Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Noncommutative symmetric functions VI: Free quasi-symmetric functions and related algebras","license":"","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"F. Hivert, G. Duchamp (University of Rouen), J.-Y. Thibon (University of Marne-la-Vallee)","submitted_at":"2001-05-09T10:04:18Z","abstract_excerpt":"This article is devoted to the study of several algebras which are related to symmetric functions, and which admit linear bases labelled by various combinatorial objects: permutations (free quasi-symmetric functions), standard Young tableaux (free symmetric functions) and packed integer matrices (matrix quasi-symmetric functions). Free quasi-symmetric functions provide a kind of noncommutative Frobenius characteristic for a certain category of modules over the 0-Hecke algebras. New examples of indecomposable $H_n(0)$-modules are discussed, and the homological properties of $H_n(0)$ are compute"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0105065","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":"math/0105065","created_at":"2026-05-18T03:34:00.590560+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0105065v1","created_at":"2026-05-18T03:34:00.590560+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0105065","created_at":"2026-05-18T03:34:00.590560+00:00"},{"alias_kind":"pith_short_12","alias_value":"KOYZZMVNDMGN","created_at":"2026-05-18T12:25:50.254431+00:00"},{"alias_kind":"pith_short_16","alias_value":"KOYZZMVNDMGN5FEF","created_at":"2026-05-18T12:25:50.254431+00:00"},{"alias_kind":"pith_short_8","alias_value":"KOYZZMVN","created_at":"2026-05-18T12:25:50.254431+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/KOYZZMVNDMGN5FEFHBDQR2CUDK","json":"https://pith.science/pith/KOYZZMVNDMGN5FEFHBDQR2CUDK.json","graph_json":"https://pith.science/api/pith-number/KOYZZMVNDMGN5FEFHBDQR2CUDK/graph.json","events_json":"https://pith.science/api/pith-number/KOYZZMVNDMGN5FEFHBDQR2CUDK/events.json","paper":"https://pith.science/paper/KOYZZMVN"},"agent_actions":{"view_html":"https://pith.science/pith/KOYZZMVNDMGN5FEFHBDQR2CUDK","download_json":"https://pith.science/pith/KOYZZMVNDMGN5FEFHBDQR2CUDK.json","view_paper":"https://pith.science/paper/KOYZZMVN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0105065&json=true","fetch_graph":"https://pith.science/api/pith-number/KOYZZMVNDMGN5FEFHBDQR2CUDK/graph.json","fetch_events":"https://pith.science/api/pith-number/KOYZZMVNDMGN5FEFHBDQR2CUDK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KOYZZMVNDMGN5FEFHBDQR2CUDK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KOYZZMVNDMGN5FEFHBDQR2CUDK/action/storage_attestation","attest_author":"https://pith.science/pith/KOYZZMVNDMGN5FEFHBDQR2CUDK/action/author_attestation","sign_citation":"https://pith.science/pith/KOYZZMVNDMGN5FEFHBDQR2CUDK/action/citation_signature","submit_replication":"https://pith.science/pith/KOYZZMVNDMGN5FEFHBDQR2CUDK/action/replication_record"}},"created_at":"2026-05-18T03:34:00.590560+00:00","updated_at":"2026-05-18T03:34:00.590560+00:00"}