{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:A6PODGXXSJ6EBG4UQATEY5DOZP","short_pith_number":"pith:A6PODGXX","schema_version":"1.0","canonical_sha256":"079ee19af7927c409b9480264c746ecbe44b411b74fa8f2f9e382c8cffa79c38","source":{"kind":"arxiv","id":"1501.04868","version":1},"attestation_state":"computed","paper":{"title":"A lattice on decreasing trees : the metasylvester lattice","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Viviane Pons","submitted_at":"2015-01-20T16:28:25Z","abstract_excerpt":"We introduce a new combinatorial structure: the metasylvester lattice on decreasing trees. It appears in the context of the $m$-Tamari lattices and other related $m$-generalizations. The metasylvester congruence has been recently introduced by Novelli and Thibon. We show that it defines a sublattice of the $m$-permutations where elements can be represented by decreasing labelled trees: the metasylvester lattice. We study the combinatorial properties of this new structure. In particular, we give different realizations of the lattice. The $m$-Tamari lattice is by definition a sublattice of our n"},"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":"1501.04868","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-01-20T16:28:25Z","cross_cats_sorted":[],"title_canon_sha256":"f8059798aa2926349aa96c172b50ddd40d3e9c1fdcf18b3d7ca7dfb3d8ea871d","abstract_canon_sha256":"5d760e1c43751b28fbcf60b6e8565b7ae385f1caf8feaed2dd538a21e15f4bfc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:02.073240Z","signature_b64":"phKA2moaBG6YQ2xvGlX7g+4wWZOqCRK76lHeqw72TlIu7PO/vIxHChkg+/3HK4VsqYjgnuCbGuygmZ39lMxOCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"079ee19af7927c409b9480264c746ecbe44b411b74fa8f2f9e382c8cffa79c38","last_reissued_at":"2026-05-18T02:29:02.072754Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:02.072754Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A lattice on decreasing trees : the metasylvester lattice","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Viviane Pons","submitted_at":"2015-01-20T16:28:25Z","abstract_excerpt":"We introduce a new combinatorial structure: the metasylvester lattice on decreasing trees. It appears in the context of the $m$-Tamari lattices and other related $m$-generalizations. The metasylvester congruence has been recently introduced by Novelli and Thibon. We show that it defines a sublattice of the $m$-permutations where elements can be represented by decreasing labelled trees: the metasylvester lattice. We study the combinatorial properties of this new structure. In particular, we give different realizations of the lattice. The $m$-Tamari lattice is by definition a sublattice of our n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.04868","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":"1501.04868","created_at":"2026-05-18T02:29:02.072833+00:00"},{"alias_kind":"arxiv_version","alias_value":"1501.04868v1","created_at":"2026-05-18T02:29:02.072833+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.04868","created_at":"2026-05-18T02:29:02.072833+00:00"},{"alias_kind":"pith_short_12","alias_value":"A6PODGXXSJ6E","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_16","alias_value":"A6PODGXXSJ6EBG4U","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_8","alias_value":"A6PODGXX","created_at":"2026-05-18T12:29:10.953037+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/A6PODGXXSJ6EBG4UQATEY5DOZP","json":"https://pith.science/pith/A6PODGXXSJ6EBG4UQATEY5DOZP.json","graph_json":"https://pith.science/api/pith-number/A6PODGXXSJ6EBG4UQATEY5DOZP/graph.json","events_json":"https://pith.science/api/pith-number/A6PODGXXSJ6EBG4UQATEY5DOZP/events.json","paper":"https://pith.science/paper/A6PODGXX"},"agent_actions":{"view_html":"https://pith.science/pith/A6PODGXXSJ6EBG4UQATEY5DOZP","download_json":"https://pith.science/pith/A6PODGXXSJ6EBG4UQATEY5DOZP.json","view_paper":"https://pith.science/paper/A6PODGXX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1501.04868&json=true","fetch_graph":"https://pith.science/api/pith-number/A6PODGXXSJ6EBG4UQATEY5DOZP/graph.json","fetch_events":"https://pith.science/api/pith-number/A6PODGXXSJ6EBG4UQATEY5DOZP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/A6PODGXXSJ6EBG4UQATEY5DOZP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/A6PODGXXSJ6EBG4UQATEY5DOZP/action/storage_attestation","attest_author":"https://pith.science/pith/A6PODGXXSJ6EBG4UQATEY5DOZP/action/author_attestation","sign_citation":"https://pith.science/pith/A6PODGXXSJ6EBG4UQATEY5DOZP/action/citation_signature","submit_replication":"https://pith.science/pith/A6PODGXXSJ6EBG4UQATEY5DOZP/action/replication_record"}},"created_at":"2026-05-18T02:29:02.072833+00:00","updated_at":"2026-05-18T02:29:02.072833+00:00"}