{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1997:DZ4TZBV54ORCTWMFFDY6OIOGRA","short_pith_number":"pith:DZ4TZBV5","schema_version":"1.0","canonical_sha256":"1e793c86bde3a229d98528f1e721c6883dfa2b9e0597c626dcd4899d97e1f6cf","source":{"kind":"arxiv","id":"math/9703209","version":1},"attestation_state":"computed","paper":{"title":"A Combinatorial proof of a result of Hetyei and Reiner on Foata-Strehl type permutation trees","license":"","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Mikl\\'os B\\'ona","submitted_at":"1997-03-25T00:00:00Z","abstract_excerpt":"We give a combinatorial proof of the result of Hetyei and Reiner that there are exactly $n!/3$ permutations of length $n$ in the minmax tree representation of which the $i$th node is a leaf. We also prove the new result that the number of $n$-permutations in which this node has one child is $n!/3$ as well, implying that the same holds for those in which this node has two children."},"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":"math/9703209","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CO","submitted_at":"1997-03-25T00:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"036a5c37917f3224671479e0a10b9488b5fe2bd3a43f69feccbe4cca9af47091","abstract_canon_sha256":"568ea647fa42c38a8d02369038b15111a1503d9b84b57a7dbf53ac9a3d666930"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:37.065725Z","signature_b64":"oQ5CnWah0WVaM/tplOIIs56zXzBpbW0M3TbDxgiHps1atY6nFhb8mHJpQlLek2FoIBLtuR4WVl7SGwXUlOyKCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1e793c86bde3a229d98528f1e721c6883dfa2b9e0597c626dcd4899d97e1f6cf","last_reissued_at":"2026-05-18T01:05:37.065294Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:37.065294Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Combinatorial proof of a result of Hetyei and Reiner on Foata-Strehl type permutation trees","license":"","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Mikl\\'os B\\'ona","submitted_at":"1997-03-25T00:00:00Z","abstract_excerpt":"We give a combinatorial proof of the result of Hetyei and Reiner that there are exactly $n!/3$ permutations of length $n$ in the minmax tree representation of which the $i$th node is a leaf. We also prove the new result that the number of $n$-permutations in which this node has one child is $n!/3$ as well, implying that the same holds for those in which this node has two children."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9703209","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":"math/9703209","created_at":"2026-05-18T01:05:37.065362+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/9703209v1","created_at":"2026-05-18T01:05:37.065362+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9703209","created_at":"2026-05-18T01:05:37.065362+00:00"},{"alias_kind":"pith_short_12","alias_value":"DZ4TZBV54ORC","created_at":"2026-05-18T12:25:48.327863+00:00"},{"alias_kind":"pith_short_16","alias_value":"DZ4TZBV54ORCTWMF","created_at":"2026-05-18T12:25:48.327863+00:00"},{"alias_kind":"pith_short_8","alias_value":"DZ4TZBV5","created_at":"2026-05-18T12:25:48.327863+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/DZ4TZBV54ORCTWMFFDY6OIOGRA","json":"https://pith.science/pith/DZ4TZBV54ORCTWMFFDY6OIOGRA.json","graph_json":"https://pith.science/api/pith-number/DZ4TZBV54ORCTWMFFDY6OIOGRA/graph.json","events_json":"https://pith.science/api/pith-number/DZ4TZBV54ORCTWMFFDY6OIOGRA/events.json","paper":"https://pith.science/paper/DZ4TZBV5"},"agent_actions":{"view_html":"https://pith.science/pith/DZ4TZBV54ORCTWMFFDY6OIOGRA","download_json":"https://pith.science/pith/DZ4TZBV54ORCTWMFFDY6OIOGRA.json","view_paper":"https://pith.science/paper/DZ4TZBV5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/9703209&json=true","fetch_graph":"https://pith.science/api/pith-number/DZ4TZBV54ORCTWMFFDY6OIOGRA/graph.json","fetch_events":"https://pith.science/api/pith-number/DZ4TZBV54ORCTWMFFDY6OIOGRA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DZ4TZBV54ORCTWMFFDY6OIOGRA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DZ4TZBV54ORCTWMFFDY6OIOGRA/action/storage_attestation","attest_author":"https://pith.science/pith/DZ4TZBV54ORCTWMFFDY6OIOGRA/action/author_attestation","sign_citation":"https://pith.science/pith/DZ4TZBV54ORCTWMFFDY6OIOGRA/action/citation_signature","submit_replication":"https://pith.science/pith/DZ4TZBV54ORCTWMFFDY6OIOGRA/action/replication_record"}},"created_at":"2026-05-18T01:05:37.065362+00:00","updated_at":"2026-05-18T01:05:37.065362+00:00"}