{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:57U6LTBXABFRYG64GMVKA7U4JB","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":"a8df7f56f38f89e5154a614981836c80b6390cf5a40b0f271154cfcc3cd94552","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-12-17T22:08:31Z","title_canon_sha256":"ef93c8126ef662fb81887be61c88dd36aeed4817221503e6841038f422564637"},"schema_version":"1.0","source":{"id":"1412.5646","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.5646","created_at":"2026-05-18T01:07:54Z"},{"alias_kind":"arxiv_version","alias_value":"1412.5646v3","created_at":"2026-05-18T01:07:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.5646","created_at":"2026-05-18T01:07:54Z"},{"alias_kind":"pith_short_12","alias_value":"57U6LTBXABFR","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"57U6LTBXABFRYG64","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"57U6LTBX","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:8b5e209bb8688141f9082e9bb9cca54f141b9754b88595ae2853f86c7de7db02","target":"graph","created_at":"2026-05-18T01:07:54Z","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 prove that the number of oscillating tableaux of length $n$ with at most $k$ columns, starting at $\\emptyset$ and ending at the one-column shape $(1^m)$, is equal to the number of standard Young tableaux of size~$n$ with $m$ columns of odd length, all columns of length at most $2k$. This refines a conjecture of Burrill, which it thereby establishes. We prove as well a \"Knuth-type\" extension stating a similar equi-enumeration result between generalised oscillating tableaux and semistandard tableaux.","authors_text":"Christian Krattenthaler (Universit\\\"at Wien)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-12-17T22:08:31Z","title":"Bijections between oscillating tableaux and (semi)standard tableaux via growth diagrams"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5646","kind":"arxiv","version":3},"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:c41b10e4629642fb4a2f313cbef9d20ac2e7c09d80d0e0f3e3a0d9aa89e0a453","target":"record","created_at":"2026-05-18T01:07:54Z","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":"a8df7f56f38f89e5154a614981836c80b6390cf5a40b0f271154cfcc3cd94552","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-12-17T22:08:31Z","title_canon_sha256":"ef93c8126ef662fb81887be61c88dd36aeed4817221503e6841038f422564637"},"schema_version":"1.0","source":{"id":"1412.5646","kind":"arxiv","version":3}},"canonical_sha256":"efe9e5cc37004b1c1bdc332aa07e9c486d5903b0581d6997ae96777ca0f01f23","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"efe9e5cc37004b1c1bdc332aa07e9c486d5903b0581d6997ae96777ca0f01f23","first_computed_at":"2026-05-18T01:07:54.223032Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:07:54.223032Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WWB7XQo5soD395xK87gei0Nf1SI0Jd/Ww26kvHJtUB+tPfGIInGu2jXPweIX9wBCXxbPArWj/JqzhfMSLMTmAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:07:54.223502Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.5646","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c41b10e4629642fb4a2f313cbef9d20ac2e7c09d80d0e0f3e3a0d9aa89e0a453","sha256:8b5e209bb8688141f9082e9bb9cca54f141b9754b88595ae2853f86c7de7db02"],"state_sha256":"c1cc5dbc25e66e071cd1df5dc4a8bf3e4b4941d1952f6156a8983819d6ba6b0a"}