{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:OTNU62XI4457CBLPCMMJUXFCYT","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":"6916acd6b4ceefd06454e66271e649861102c2b29adb73a49abb4da66d507c93","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-06-08T05:02:19Z","title_canon_sha256":"ec18d3ad55d628c48f1dbf8d776bcab250aedcbc72cc7bc8b63cca1a04a03b54"},"schema_version":"1.0","source":{"id":"1106.1498","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.1498","created_at":"2026-05-18T02:21:44Z"},{"alias_kind":"arxiv_version","alias_value":"1106.1498v2","created_at":"2026-05-18T02:21:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.1498","created_at":"2026-05-18T02:21:44Z"},{"alias_kind":"pith_short_12","alias_value":"OTNU62XI4457","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"OTNU62XI4457CBLP","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"OTNU62XI","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:b3561243094ac1267096a3a544a67d5ce48482776ab9d438df3e1763e9953cd4","target":"graph","created_at":"2026-05-18T02:21:44Z","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":"An m-ballot path of size n is a path on the square grid consisting of north and east steps, starting at (0,0), ending at (mn,n), and never going below the line {x=my}. The set of these paths can be equipped with a lattice structure, called the m-Tamari lattice, which generalizes the usual Tamari lattice obtained when m=1. We prove that the number of intervals in this lattice is $$ \\frac {m+1}{n(mn+1)} {(m+1)^2 n+m\\choose n-1}. $$ This formula was recently conjectured by Bergeron in connection with the study of coinvariant spaces. The case m=1 was proved a few years ago by Chapoton. Our proof i","authors_text":"Eric Fusy (LIX), Louis-Fran\\c{c}ois Pr\\'eville Ratelle, Mireille Bousquet-M\\'elou (LaBRI)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-06-08T05:02:19Z","title":"The number of intervals in the m-Tamari lattices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.1498","kind":"arxiv","version":2},"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:a396d8b591abc980c41b8a1fa30a6f8c8eb6078ee9035a7e941e4027543a9946","target":"record","created_at":"2026-05-18T02:21:44Z","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":"6916acd6b4ceefd06454e66271e649861102c2b29adb73a49abb4da66d507c93","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-06-08T05:02:19Z","title_canon_sha256":"ec18d3ad55d628c48f1dbf8d776bcab250aedcbc72cc7bc8b63cca1a04a03b54"},"schema_version":"1.0","source":{"id":"1106.1498","kind":"arxiv","version":2}},"canonical_sha256":"74db4f6ae8e73bf1056f13189a5ca2c4e5a7cd500e3d2e54bd0a2be9943ddb66","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"74db4f6ae8e73bf1056f13189a5ca2c4e5a7cd500e3d2e54bd0a2be9943ddb66","first_computed_at":"2026-05-18T02:21:44.036342Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:21:44.036342Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QHoT8fFlii67HHwXj0L1HUGNvzow5LICa27NW2r1wiAXgGjqXEldvXEP+LSip3Ik/MwfaMZioxq4YYUligniBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:21:44.036785Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.1498","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a396d8b591abc980c41b8a1fa30a6f8c8eb6078ee9035a7e941e4027543a9946","sha256:b3561243094ac1267096a3a544a67d5ce48482776ab9d438df3e1763e9953cd4"],"state_sha256":"5ccdd4fff17c8871b872d134495cd782657e7ce19cc0e3f3be4022ce1af0aafd"}