An F-polygon is a simple polygon whose vertices are F-points, which are points of the set of vertices of a tiling of R~2 by regular triangles and regular hexagons of unit edge. Let f(v) denote the least possible numbe...An F-polygon is a simple polygon whose vertices are F-points, which are points of the set of vertices of a tiling of R~2 by regular triangles and regular hexagons of unit edge. Let f(v) denote the least possible number of F-points in the interior of a convex F-polygon K with v vertices. In this paper we prove that f(10) = 10, f(11) = 12,f(12) = 12.展开更多
An interior point of a finite planar point set is a point of the set that is not on the boundary of the convex hull of the set. For any integer k ≥ 1, let h（κ） be the smallest integer such that every set of points...An interior point of a finite planar point set is a point of the set that is not on the boundary of the convex hull of the set. For any integer k ≥ 1, let h（κ） be the smallest integer such that every set of points in the plane, no three collinear, with at least h（κ） interior points, has a subset of points with exactly κ or κ ＋ 1 interior points of P. We prove that h（5）=11.展开更多
基金Supported by National Natural Science Foundation of China(Grant No.12271139)。
文摘An F-polygon is a simple polygon whose vertices are F-points, which are points of the set of vertices of a tiling of R~2 by regular triangles and regular hexagons of unit edge. Let f(v) denote the least possible number of F-points in the interior of a convex F-polygon K with v vertices. In this paper we prove that f(10) = 10, f(11) = 12,f(12) = 12.
基金Supported by the National Natural Science Foundation of China(10901045,11171088)Supported by the NSF of Hebei Province(A2010000828)Supported by the SF of Hebei University of Science and Technology(QD200955)
文摘An interior point of a finite planar point set is a point of the set that is not on the boundary of the convex hull of the set. For any integer k ≥ 1, let h（κ） be the smallest integer such that every set of points in the plane, no three collinear, with at least h（κ） interior points, has a subset of points with exactly κ or κ ＋ 1 interior points of P. We prove that h（5）=11.
