{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:GFMR23MNEFCTGMI53Q66UEMXAK","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":"b98d2958b7fcc6924d7d2cb7e01b6690114088e43b2ed02839c5a7fce3beeb5a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-06T09:23:40Z","title_canon_sha256":"b44d69698e8f4524ccf84fcbdf35f605593d1ffdb561ba25068cfbf7b0235b82"},"schema_version":"1.0","source":{"id":"1406.1616","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.1616","created_at":"2026-05-18T02:50:22Z"},{"alias_kind":"arxiv_version","alias_value":"1406.1616v1","created_at":"2026-05-18T02:50:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.1616","created_at":"2026-05-18T02:50:22Z"},{"alias_kind":"pith_short_12","alias_value":"GFMR23MNEFCT","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"GFMR23MNEFCTGMI5","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"GFMR23MN","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:268e6b41b55320f878870d896a05a197d21f955f42139f66be460229918a0e40","target":"graph","created_at":"2026-05-18T02:50:22Z","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":"The Fuss-Catalan numbers are a generalization of the Catalan numbers. They enumerate a large class of objects and in particular m-Dyck paths and m+1-ary trees. Recently, F. Bergeron defined an analogue for generic m of the Tamari order on classical Dyck words. The author and J.-Y. Thibon showed that the combinatorial Hopf algebras related to these m-Tamari orders are defined thanks to the same monoid, the sylvester monoid, as in the m=1 case and that all related Hopf algebras also have m analogues.\n  We present here the m-generalization of another construction on Catalan sets: the dendriform a","authors_text":"Jean-Christophe Novelli","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-06T09:23:40Z","title":"m-dendriform algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.1616","kind":"arxiv","version":1},"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":"sha256:8dfefef8fcb87060d32dce6a3c7fc2e7a92bcbee63b957822e358945d9dd4ca6","target":"record","created_at":"2026-05-18T02:50:22Z","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":"b98d2958b7fcc6924d7d2cb7e01b6690114088e43b2ed02839c5a7fce3beeb5a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-06T09:23:40Z","title_canon_sha256":"b44d69698e8f4524ccf84fcbdf35f605593d1ffdb561ba25068cfbf7b0235b82"},"schema_version":"1.0","source":{"id":"1406.1616","kind":"arxiv","version":1}},"canonical_sha256":"31591d6d8d214533311ddc3dea1197028848260da0c6531392e96e0216516a69","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"31591d6d8d214533311ddc3dea1197028848260da0c6531392e96e0216516a69","first_computed_at":"2026-05-18T02:50:22.051812Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:50:22.051812Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xTc1qN73VKHvN/2TF3LwKZQOeuMIQpduIiad6bxzeMFwscGT+L6amrDpTg1bpqG6LUzpWHPXU4sWUHYRGN45Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T02:50:22.052325Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.1616","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8dfefef8fcb87060d32dce6a3c7fc2e7a92bcbee63b957822e358945d9dd4ca6","sha256:268e6b41b55320f878870d896a05a197d21f955f42139f66be460229918a0e40"],"state_sha256":"f5eed742175304f66381892ab867519ed644993dfaee57303b613a57e780e4c7"}