{"paper":{"title":"The enumeration of generalized Tamari intervals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Louis-Fran\\c{c}ois Pr\\'eville-Ratelle, Wenjie Fang","submitted_at":"2015-11-18T20:38:27Z","abstract_excerpt":"Let $v$ be a grid path made of north and east steps. The lattice $\\rm{T{\\scriptsize AM}}(v)$, based on all grid paths weakly above $v$ and sharing the same endpoints as $v$, was introduced by Pr\\'eville-Ratelle and Viennot (2014) and corresponds to the usual Tamari lattice in the case $v=(NE)^n$. Our main contribution is that the enumeration of intervals in $\\rm{T{\\scriptsize AM}}(v)$, over all $v$ of length $n$, is given by $\\frac{2 (3n+3)!}{(n+2)! (2n+3)!}$. This formula was first obtained by Tutte(1963) for the enumeration of non-separable planar maps. Moreover, we give an explicit bijectio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.05937","kind":"arxiv","version":3},"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"}