{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:ZUMLIP2ECF5ZNCXU2XSZ5IHJZJ","short_pith_number":"pith:ZUMLIP2E","schema_version":"1.0","canonical_sha256":"cd18b43f44117b968af4d5e59ea0e9ca62602672af57b6aa40431e1ca285e5db","source":{"kind":"arxiv","id":"0809.4480","version":1},"attestation_state":"computed","paper":{"title":"Inversion of some series of free quasi-symmetric functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Florent Hivert, Jean-Christophe Novelli, Jean-Yves Thibon","submitted_at":"2008-09-25T19:35:08Z","abstract_excerpt":"We give a combinatorial formula for the inverses of the alternating sums of free quasi-symmetric functions of the form F_{\\omega(I)} where I runs over compositions with parts in a prescribed set C. This proves in particular three special cases (no restriction, even parts, and all parts equal to 2) which were conjectured by B. C. V. Ung in [Proc. FPSAC'98, Toronto]."},"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":"0809.4480","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2008-09-25T19:35:08Z","cross_cats_sorted":[],"title_canon_sha256":"569e0aba4256fc72cf263b5a1ec970adf99855a02f806745586554795c11a104","abstract_canon_sha256":"b0f2083db36573f555ab9bd290c7c2aeb746b817b887417b480ddf1061722ad8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:34:12.516802Z","signature_b64":"oVBo+wanpVTp2iw7IX/hcZ872LOOXSxasJOeK81AThTHwVmPnZRMk0PTy4jDrEOLsx6iCJOXsA46dJV7FFFNBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cd18b43f44117b968af4d5e59ea0e9ca62602672af57b6aa40431e1ca285e5db","last_reissued_at":"2026-05-18T03:34:12.516185Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:34:12.516185Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Inversion of some series of free quasi-symmetric functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Florent Hivert, Jean-Christophe Novelli, Jean-Yves Thibon","submitted_at":"2008-09-25T19:35:08Z","abstract_excerpt":"We give a combinatorial formula for the inverses of the alternating sums of free quasi-symmetric functions of the form F_{\\omega(I)} where I runs over compositions with parts in a prescribed set C. This proves in particular three special cases (no restriction, even parts, and all parts equal to 2) which were conjectured by B. C. V. Ung in [Proc. FPSAC'98, Toronto]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0809.4480","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":"0809.4480","created_at":"2026-05-18T03:34:12.516281+00:00"},{"alias_kind":"arxiv_version","alias_value":"0809.4480v1","created_at":"2026-05-18T03:34:12.516281+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0809.4480","created_at":"2026-05-18T03:34:12.516281+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZUMLIP2ECF5Z","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZUMLIP2ECF5ZNCXU","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZUMLIP2E","created_at":"2026-05-18T12:25:58.018023+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/ZUMLIP2ECF5ZNCXU2XSZ5IHJZJ","json":"https://pith.science/pith/ZUMLIP2ECF5ZNCXU2XSZ5IHJZJ.json","graph_json":"https://pith.science/api/pith-number/ZUMLIP2ECF5ZNCXU2XSZ5IHJZJ/graph.json","events_json":"https://pith.science/api/pith-number/ZUMLIP2ECF5ZNCXU2XSZ5IHJZJ/events.json","paper":"https://pith.science/paper/ZUMLIP2E"},"agent_actions":{"view_html":"https://pith.science/pith/ZUMLIP2ECF5ZNCXU2XSZ5IHJZJ","download_json":"https://pith.science/pith/ZUMLIP2ECF5ZNCXU2XSZ5IHJZJ.json","view_paper":"https://pith.science/paper/ZUMLIP2E","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0809.4480&json=true","fetch_graph":"https://pith.science/api/pith-number/ZUMLIP2ECF5ZNCXU2XSZ5IHJZJ/graph.json","fetch_events":"https://pith.science/api/pith-number/ZUMLIP2ECF5ZNCXU2XSZ5IHJZJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZUMLIP2ECF5ZNCXU2XSZ5IHJZJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZUMLIP2ECF5ZNCXU2XSZ5IHJZJ/action/storage_attestation","attest_author":"https://pith.science/pith/ZUMLIP2ECF5ZNCXU2XSZ5IHJZJ/action/author_attestation","sign_citation":"https://pith.science/pith/ZUMLIP2ECF5ZNCXU2XSZ5IHJZJ/action/citation_signature","submit_replication":"https://pith.science/pith/ZUMLIP2ECF5ZNCXU2XSZ5IHJZJ/action/replication_record"}},"created_at":"2026-05-18T03:34:12.516281+00:00","updated_at":"2026-05-18T03:34:12.516281+00:00"}