{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:DGSQUZKROUAEKJOP5RAEFWI25E","short_pith_number":"pith:DGSQUZKR","schema_version":"1.0","canonical_sha256":"19a50a655175004525cfec4042d91ae92724a85acac4c9d1505f0e69e91128d3","source":{"kind":"arxiv","id":"1101.4332","version":2},"attestation_state":"computed","paper":{"title":"Mahonian Pairs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bruce E. Sagan (Department of Mathematics, Carla D. Savage (Department of Computer Science, East Lansing, MI, Michigan State University, NC, North Carolina State University, Raleigh, USA)","submitted_at":"2011-01-22T23:14:08Z","abstract_excerpt":"We introduce the notion of a Mahonian pair. Consider the set, P^*, of all words having the positive integers as alphabet. Given finite subsets S,T of P^*, we say that (S,T) is a Mahonian pair if the distribution of the major index, maj, over S is the same as the distribution of the inversion number, inv, over T. So the well-known fact that maj and inv are equidistributed over the symmetric group, S_n, can be expressed by saying that (S_n,S_n) is a Mahonian pair. We investigate various Mahonian pairs (S,T) with S different from T. Our principal tool is Foata's fundamental bijection f: P^* -> P^"},"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":"1101.4332","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-01-22T23:14:08Z","cross_cats_sorted":[],"title_canon_sha256":"4b0248fbb445e887fb04aeeb85cce833547e4eaaa6e621459c3dd029f0132245","abstract_canon_sha256":"595520612cd833aa4d7cb0cf5b9b5375e9b6a1717c94bd72b80f955720de882f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:09:45.809121Z","signature_b64":"sePBigm61q3vCRtInPlrC8dX6WFeMCSLDbTaRwsqu0XJ+RcQlZi4dxYzw5vnWlR0mn5UDilPBjKLzc2jGsfWCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"19a50a655175004525cfec4042d91ae92724a85acac4c9d1505f0e69e91128d3","last_reissued_at":"2026-05-18T04:09:45.808752Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:09:45.808752Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Mahonian Pairs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bruce E. Sagan (Department of Mathematics, Carla D. Savage (Department of Computer Science, East Lansing, MI, Michigan State University, NC, North Carolina State University, Raleigh, USA)","submitted_at":"2011-01-22T23:14:08Z","abstract_excerpt":"We introduce the notion of a Mahonian pair. Consider the set, P^*, of all words having the positive integers as alphabet. Given finite subsets S,T of P^*, we say that (S,T) is a Mahonian pair if the distribution of the major index, maj, over S is the same as the distribution of the inversion number, inv, over T. So the well-known fact that maj and inv are equidistributed over the symmetric group, S_n, can be expressed by saying that (S_n,S_n) is a Mahonian pair. We investigate various Mahonian pairs (S,T) with S different from T. Our principal tool is Foata's fundamental bijection f: P^* -> P^"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.4332","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":"1101.4332","created_at":"2026-05-18T04:09:45.808806+00:00"},{"alias_kind":"arxiv_version","alias_value":"1101.4332v2","created_at":"2026-05-18T04:09:45.808806+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.4332","created_at":"2026-05-18T04:09:45.808806+00:00"},{"alias_kind":"pith_short_12","alias_value":"DGSQUZKROUAE","created_at":"2026-05-18T12:26:26.731475+00:00"},{"alias_kind":"pith_short_16","alias_value":"DGSQUZKROUAEKJOP","created_at":"2026-05-18T12:26:26.731475+00:00"},{"alias_kind":"pith_short_8","alias_value":"DGSQUZKR","created_at":"2026-05-18T12:26:26.731475+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/DGSQUZKROUAEKJOP5RAEFWI25E","json":"https://pith.science/pith/DGSQUZKROUAEKJOP5RAEFWI25E.json","graph_json":"https://pith.science/api/pith-number/DGSQUZKROUAEKJOP5RAEFWI25E/graph.json","events_json":"https://pith.science/api/pith-number/DGSQUZKROUAEKJOP5RAEFWI25E/events.json","paper":"https://pith.science/paper/DGSQUZKR"},"agent_actions":{"view_html":"https://pith.science/pith/DGSQUZKROUAEKJOP5RAEFWI25E","download_json":"https://pith.science/pith/DGSQUZKROUAEKJOP5RAEFWI25E.json","view_paper":"https://pith.science/paper/DGSQUZKR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1101.4332&json=true","fetch_graph":"https://pith.science/api/pith-number/DGSQUZKROUAEKJOP5RAEFWI25E/graph.json","fetch_events":"https://pith.science/api/pith-number/DGSQUZKROUAEKJOP5RAEFWI25E/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DGSQUZKROUAEKJOP5RAEFWI25E/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DGSQUZKROUAEKJOP5RAEFWI25E/action/storage_attestation","attest_author":"https://pith.science/pith/DGSQUZKROUAEKJOP5RAEFWI25E/action/author_attestation","sign_citation":"https://pith.science/pith/DGSQUZKROUAEKJOP5RAEFWI25E/action/citation_signature","submit_replication":"https://pith.science/pith/DGSQUZKROUAEKJOP5RAEFWI25E/action/replication_record"}},"created_at":"2026-05-18T04:09:45.808806+00:00","updated_at":"2026-05-18T04:09:45.808806+00:00"}