{"paper":{"title":"The number of intervals in the m-Tamari lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Eric Fusy (LIX), Louis-Fran\\c{c}ois Pr\\'eville Ratelle, Mireille Bousquet-M\\'elou (LaBRI)","submitted_at":"2011-06-08T05:02:19Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.1498","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"}