{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:GFSPCOFNW42WQTYBLI4J757NGK","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"917ec09cad36a22cc56e9bacbb7cf767d9e3811c1d175159c75ed57522cb1d50","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-10-11T19:44:38Z","title_canon_sha256":"2a4d876c75da239de7751d3df7c122440d3d58f5c02ed3d50d54d0366746468b"},"schema_version":"1.0","source":{"id":"0910.2036","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.2036","created_at":"2026-05-18T04:14:38Z"},{"alias_kind":"arxiv_version","alias_value":"0910.2036v2","created_at":"2026-05-18T04:14:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.2036","created_at":"2026-05-18T04:14:38Z"},{"alias_kind":"pith_short_12","alias_value":"GFSPCOFNW42W","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"GFSPCOFNW42WQTYB","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"GFSPCOFN","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:9cd11f5fcff3883c1661a22151d687515dd7541d0488004dd7e319d8187bba4c","target":"graph","created_at":"2026-05-18T04:14:38Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We interpret noncrossing partitions of type $B$ and type $D$ in terms of noncrossing partitions of type $A$. As an application, we get type-preserving bijections between noncrossing and nonnesting partitions of type $B$, type $C$ and type $D$ which are different from those in the recent work of Fink and Giraldo. We also define Catalan tableaux of type $B$ and type $D$, and find bijections between them and noncrossing partitions of type $B$ and type $D$ respectively.","authors_text":"Jang Soo Kim","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-10-11T19:44:38Z","title":"New interpretations for noncrossing partitions of classical types"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.2036","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:bd26aebefcd01dcbb9bcdf0d16524ab8655f08c89e4eb8c83fb8933b7e9193d7","target":"record","created_at":"2026-05-18T04:14:38Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"917ec09cad36a22cc56e9bacbb7cf767d9e3811c1d175159c75ed57522cb1d50","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-10-11T19:44:38Z","title_canon_sha256":"2a4d876c75da239de7751d3df7c122440d3d58f5c02ed3d50d54d0366746468b"},"schema_version":"1.0","source":{"id":"0910.2036","kind":"arxiv","version":2}},"canonical_sha256":"3164f138adb735684f015a389ff7ed32bee07d3b5c93891fa8a592262f6ca685","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3164f138adb735684f015a389ff7ed32bee07d3b5c93891fa8a592262f6ca685","first_computed_at":"2026-05-18T04:14:38.296529Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:14:38.296529Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JLJveISmwMH6LJNYe3y8YIW+DdPoC6HUOUvvchGUr2bUCpI7K8wbQvaFfbLDCWFHmTivbD2wX+52pGenjAEZBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:14:38.297080Z","signed_message":"canonical_sha256_bytes"},"source_id":"0910.2036","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bd26aebefcd01dcbb9bcdf0d16524ab8655f08c89e4eb8c83fb8933b7e9193d7","sha256:9cd11f5fcff3883c1661a22151d687515dd7541d0488004dd7e319d8187bba4c"],"state_sha256":"9237a490a926cfda90dd5e17c26e5a676914c17f2a8165d683191c3a505b8976"}