A triangulation T of a convex n-gon P is a dissection of P into triangles by noncrossing diagonals. An ear in such a triangulation is a triangle of T that shares two sides with P itself. Certain enumerative 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.
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