کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4656445 1343437 2006 35 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On empty convex polygons in a planar point set
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات گسسته و ترکیبات
پیش نمایش صفحه اول مقاله
On empty convex polygons in a planar point set
چکیده انگلیسی

Let P be a set of n points in general position in the plane. Let Xk(P) denote the number of empty convex k-gons determined by P. We derive, using elementary proof techniques, several equalities and inequalities involving the quantities Xk(P) and several related quantities. Most of these equalities and inequalities are new, except for a few that have been proved earlier using a considerably more complex machinery from matroid and polytope theory, and algebraic topology. Some of these relationships are also extended to higher dimensions. We present several implications of these relationships, and discuss their connection with several long-standing open problems, the most notorious of which is the existence of an empty convex hexagon in any point set with sufficiently many points.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Combinatorial Theory, Series A - Volume 113, Issue 3, April 2006, Pages 385-419