Half-Simple Symmetric Venn Diagrams
نویسندگان
چکیده
A Venn diagram is simple if at most two curves intersect at any given point. A recent paper of Griggs, Killian, and Savage [Elec. J. Combinatorics, Research Paper 2, 2004] shows how to construct rotationally symmetric Venn diagrams for any prime number of curves. However, the resulting diagrams contain only ( n bn/2c ) intersection points, whereas a simple Venn diagram contains 2n − 2 intersection points. We show how to modify their construction to give symmetric Venn diagrams with asymptotically at least 2n−1 intersection points, whence the name “half-simple.”
منابع مشابه
New Roses: Simple Symmetric Venn Diagrams with 11 and 13 Curves
A symmetric n-Venn diagram is one that is invariant under n-fold rotation, up to a relabeling of curves. A simple n-Venn diagram is an n-Venn diagram in which at most two curves intersect at any point. In this paper, we introduce a new property of Venn diagrams called crosscut symmetry, which is related to dihedral symmetry. Utilizing a computer search restricted to diagrams with crosscut symme...
متن کاملThe Search for Symmetric Venn Diagrams
Given a family C = {C 1 , C 2 , ..., C n } of n simple (Jordan) curves which intersect pairwise in finitely many points, we say that it is an independent family if each of the 2 n sets is not empty, where X j denotes one of the two connected components of the complement of C j (that is, each X j is either the interior or the exterior of C j). If, moreover, each of the sets in (*) is connected, ...
متن کاملSymmetric Monotone Venn Diagrams with Seven Curves
An n-Venn diagram consists of n curves drawn in the plane in such a way that each of the 2 possible intersections of the interiors and exteriors of the curves forms a connected non-empty region. A k-region in a diagram is a region that is in the interior of precisely k curves. A n-Venn diagram is symmetric if it has a point of rotation about which rotations of the plane by 2π/n radians leaves t...
متن کاملWhich n-Venn diagrams can be drawn with convex k-gons?
We establish a new lower bound for the number of sides required for the component curves of simple Venn diagrams made from polygons. Specifically, for any n-Venn diagram of convex k-gons, we prove that k ≥ (2 − 2 − n)/(n(n − 2)). In the process we prove that Venn diagrams of seven curves, simple or not, cannot be formed from triangles. We then give an example achieving the new lower bound of a ...
متن کاملA New Rose : The First Simple Symmetric 11-Venn Diagram
A symmetric Venn diagram is one that is invariant under rotation, up to a relabeling of curves. A simple Venn diagram is one in which at most two curves intersect at any point. In this paper we introduce a new property of Venn diagrams called crosscut symmetry, which is related to dihedral symmetry. Utilizing a computer search restricted to crosscut symmetry we found many simple symmetric Venn ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Electr. J. Comb.
دوره 11 شماره
صفحات -
تاریخ انتشار 2004