{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:GL3DTFRXFYW56CUAXY6BD5PQDL","short_pith_number":"pith:GL3DTFRX","schema_version":"1.0","canonical_sha256":"32f63996372e2ddf0a80be3c11f5f01ac00246377d98661570ba41a953e294a1","source":{"kind":"arxiv","id":"1504.06894","version":2},"attestation_state":"computed","paper":{"title":"A bijective enumeration of $3$-strip tableaux","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Emma Yu Jin","submitted_at":"2015-04-26T23:30:57Z","abstract_excerpt":"Baryshnikov and Romik derived the combinatorial identities for the numbers of the $m$-strip tableaux. This generalized the classical Andr\\'e's theorem for the number of up-down permutations. They asked for a bijective proof for the enumeration of $3$-strip tableaux. In this paper we will provide such a bijective proof. First we count the $3$-strip tableaux by decomposition. Secondly we will apply this \"decomposition\" idea on the up-down permutations and down-up permutations to enumerate the $3$-strip tableaux bijectively."},"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":"1504.06894","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-04-26T23:30:57Z","cross_cats_sorted":[],"title_canon_sha256":"78d0bd4c6c548b425bde9527cd7e2f65fd9513d728465eb615ad40d3c6a05eb0","abstract_canon_sha256":"e92de9dcc8c5f96a7e66a8b58c16f21cf7f0a8db364d7230f9f392e260632e4a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:03:45.005562Z","signature_b64":"DPhrXFnIDAP1S+MpmlQdSNWtMZN7PG82NQ2wfPx4yDPpQpJVWH6S7qWY33XPpjPGcMNeI5pPgWXZ7NqxLvXnDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"32f63996372e2ddf0a80be3c11f5f01ac00246377d98661570ba41a953e294a1","last_reissued_at":"2026-05-18T02:03:45.004896Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:03:45.004896Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A bijective enumeration of $3$-strip tableaux","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Emma Yu Jin","submitted_at":"2015-04-26T23:30:57Z","abstract_excerpt":"Baryshnikov and Romik derived the combinatorial identities for the numbers of the $m$-strip tableaux. This generalized the classical Andr\\'e's theorem for the number of up-down permutations. They asked for a bijective proof for the enumeration of $3$-strip tableaux. In this paper we will provide such a bijective proof. First we count the $3$-strip tableaux by decomposition. Secondly we will apply this \"decomposition\" idea on the up-down permutations and down-up permutations to enumerate the $3$-strip tableaux bijectively."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.06894","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":"1504.06894","created_at":"2026-05-18T02:03:45.004987+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.06894v2","created_at":"2026-05-18T02:03:45.004987+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.06894","created_at":"2026-05-18T02:03:45.004987+00:00"},{"alias_kind":"pith_short_12","alias_value":"GL3DTFRXFYW5","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_16","alias_value":"GL3DTFRXFYW56CUA","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_8","alias_value":"GL3DTFRX","created_at":"2026-05-18T12:29:22.688609+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/GL3DTFRXFYW56CUAXY6BD5PQDL","json":"https://pith.science/pith/GL3DTFRXFYW56CUAXY6BD5PQDL.json","graph_json":"https://pith.science/api/pith-number/GL3DTFRXFYW56CUAXY6BD5PQDL/graph.json","events_json":"https://pith.science/api/pith-number/GL3DTFRXFYW56CUAXY6BD5PQDL/events.json","paper":"https://pith.science/paper/GL3DTFRX"},"agent_actions":{"view_html":"https://pith.science/pith/GL3DTFRXFYW56CUAXY6BD5PQDL","download_json":"https://pith.science/pith/GL3DTFRXFYW56CUAXY6BD5PQDL.json","view_paper":"https://pith.science/paper/GL3DTFRX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.06894&json=true","fetch_graph":"https://pith.science/api/pith-number/GL3DTFRXFYW56CUAXY6BD5PQDL/graph.json","fetch_events":"https://pith.science/api/pith-number/GL3DTFRXFYW56CUAXY6BD5PQDL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GL3DTFRXFYW56CUAXY6BD5PQDL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GL3DTFRXFYW56CUAXY6BD5PQDL/action/storage_attestation","attest_author":"https://pith.science/pith/GL3DTFRXFYW56CUAXY6BD5PQDL/action/author_attestation","sign_citation":"https://pith.science/pith/GL3DTFRXFYW56CUAXY6BD5PQDL/action/citation_signature","submit_replication":"https://pith.science/pith/GL3DTFRXFYW56CUAXY6BD5PQDL/action/replication_record"}},"created_at":"2026-05-18T02:03:45.004987+00:00","updated_at":"2026-05-18T02:03:45.004987+00:00"}