2013/09/03 by Andrei Asinowski, Asinowski, Andrei, Alon Regev +1
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Advanced Graph Theory Research #Combinatorics #Combinatorics (math.CO) #Disjoint sets #FOS: Mathematics #Geometry #Mathematics #Regular polygon #Symmetry (geometry) #Topological and Geometric Data Analysis #Tree (set theory) #Triangulation #math.CO
paper · pdf · doi:10.48550/arxiv.1309.0743
openalex publication_date 2013/09/03 · arxiv created 2014/02/04 · arxiv updated 2014/02/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.