{"paper":{"title":"Triangulations with few ears: symmetry classes and disjointness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alon Regev, Andrei Asinowski","submitted_at":"2013-09-03T16:59:51Z","abstract_excerpt":"An ear in a triangulation $T$ of a convex $n$-gon $P$ is a triangle of $T$ that shares two sides with $P$ itself. Certain enumerational and structural problems become easier when one considers only triangulations with few ears. We demonstrate this in two ways. First, for $k=2, 3$, we find the number of symmetry classes of triangulations with $k$ ears. Second, for $k=2, 3$, we determine the number of triangulations disjoint from a given triangulation: this number depends only on $n$ for $k=2$, and only on lengths of branches of the dual tree for $k=3$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.0743","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"}