{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:7RNJRU7THVLU63M3M7FLZ2RD3S","short_pith_number":"pith:7RNJRU7T","schema_version":"1.0","canonical_sha256":"fc5a98d3f33d574f6d9b67cabcea23dca0d9c4f2d8dfb3d7f902f7ddc1061069","source":{"kind":"arxiv","id":"1804.01762","version":2},"attestation_state":"computed","paper":{"title":"A noncommutative cycle index and new bases of quasi-symmetric functions and noncommutative symmetric functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Frederic Toumazet, Jean-Christophe Novelli, Jean-Yves Thibon","submitted_at":"2018-04-05T10:26:25Z","abstract_excerpt":"We define a new basis of the algebra of quasi-symmetric functions by lifting the cycle-index polynomials of symmetric groups to noncommutative polynomials with coefficients in the algebra of free quasi-symmetric functions, and then projecting the coefficients to $QSym$. By duality, we obtain a basis of noncommutative symmetric functions, for which a product formula and a recurrence in the form of a combinatorial complex are obtained. This basis allows to identify noncommutative symmetric functions with the quotient of FQSym induced by the pattern-replacement relation $321 \\equiv 231$ and $312 "},"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":"1804.01762","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-04-05T10:26:25Z","cross_cats_sorted":[],"title_canon_sha256":"58af71569c56cde4292970c1ad91ecadbe128c211f01c3dfa39b138cfb2c09ab","abstract_canon_sha256":"d580762caa716c92a4841cbf8e8cf6f90c3035e8a334ae3dc0ad41ccc48e8d07"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:28.280726Z","signature_b64":"elpxE9c469E8A1HN+ksSZuBZBb32UM4YD++JpymWJssE7G0dAVahgWbn9+zBw3W8FN4LciO1IVP7PyujBCtbDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc5a98d3f33d574f6d9b67cabcea23dca0d9c4f2d8dfb3d7f902f7ddc1061069","last_reissued_at":"2026-05-17T23:50:28.280185Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:28.280185Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A noncommutative cycle index and new bases of quasi-symmetric functions and noncommutative symmetric functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Frederic Toumazet, Jean-Christophe Novelli, Jean-Yves Thibon","submitted_at":"2018-04-05T10:26:25Z","abstract_excerpt":"We define a new basis of the algebra of quasi-symmetric functions by lifting the cycle-index polynomials of symmetric groups to noncommutative polynomials with coefficients in the algebra of free quasi-symmetric functions, and then projecting the coefficients to $QSym$. By duality, we obtain a basis of noncommutative symmetric functions, for which a product formula and a recurrence in the form of a combinatorial complex are obtained. This basis allows to identify noncommutative symmetric functions with the quotient of FQSym induced by the pattern-replacement relation $321 \\equiv 231$ and $312 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.01762","kind":"arxiv","version":2},"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":"1804.01762","created_at":"2026-05-17T23:50:28.280269+00:00"},{"alias_kind":"arxiv_version","alias_value":"1804.01762v2","created_at":"2026-05-17T23:50:28.280269+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.01762","created_at":"2026-05-17T23:50:28.280269+00:00"},{"alias_kind":"pith_short_12","alias_value":"7RNJRU7THVLU","created_at":"2026-05-18T12:32:11.075285+00:00"},{"alias_kind":"pith_short_16","alias_value":"7RNJRU7THVLU63M3","created_at":"2026-05-18T12:32:11.075285+00:00"},{"alias_kind":"pith_short_8","alias_value":"7RNJRU7T","created_at":"2026-05-18T12:32:11.075285+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/7RNJRU7THVLU63M3M7FLZ2RD3S","json":"https://pith.science/pith/7RNJRU7THVLU63M3M7FLZ2RD3S.json","graph_json":"https://pith.science/api/pith-number/7RNJRU7THVLU63M3M7FLZ2RD3S/graph.json","events_json":"https://pith.science/api/pith-number/7RNJRU7THVLU63M3M7FLZ2RD3S/events.json","paper":"https://pith.science/paper/7RNJRU7T"},"agent_actions":{"view_html":"https://pith.science/pith/7RNJRU7THVLU63M3M7FLZ2RD3S","download_json":"https://pith.science/pith/7RNJRU7THVLU63M3M7FLZ2RD3S.json","view_paper":"https://pith.science/paper/7RNJRU7T","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1804.01762&json=true","fetch_graph":"https://pith.science/api/pith-number/7RNJRU7THVLU63M3M7FLZ2RD3S/graph.json","fetch_events":"https://pith.science/api/pith-number/7RNJRU7THVLU63M3M7FLZ2RD3S/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7RNJRU7THVLU63M3M7FLZ2RD3S/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7RNJRU7THVLU63M3M7FLZ2RD3S/action/storage_attestation","attest_author":"https://pith.science/pith/7RNJRU7THVLU63M3M7FLZ2RD3S/action/author_attestation","sign_citation":"https://pith.science/pith/7RNJRU7THVLU63M3M7FLZ2RD3S/action/citation_signature","submit_replication":"https://pith.science/pith/7RNJRU7THVLU63M3M7FLZ2RD3S/action/replication_record"}},"created_at":"2026-05-17T23:50:28.280269+00:00","updated_at":"2026-05-17T23:50:28.280269+00:00"}