{"paper":{"title":"Geometry of $\\nu$-Tamari lattices in types $A$ and $B$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Arnau Padrol, Camilo Sarmiento, Cesar Ceballos","submitted_at":"2016-11-29T19:16:07Z","abstract_excerpt":"In this paper, we exploit the combinatorics and geometry of triangulations of products of simplices to derive new results in the context of Catalan combinatorics of $\\nu$-Tamari lattices. In our framework, the main role of \"Catalan objects\" is played by $(I,\\overline{J})$-trees: bipartite trees associated to a pair $(I,\\overline{J})$ of finite index sets that stand in simple bijection with lattice paths weakly above a lattice path $\\nu=\\nu(I,\\overline{J})$. Such trees label the maximal simplices of a triangulation whose dual polyhedral complex gives a geometric realization of the $\\nu$-Tamari "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.09794","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"}