Half-simple symmetric Venn diagrams
Summary: A Venn diagram is simple if at most two curves intersect at any given point. A recent paper of \textit{J. Griggs} et al. [Electron. J. Comb., Research paper R2 (2004; Zbl 1034.06001)] shows how to construct rotationally symmetric Venn diagrams for any prime number of curves. However, the resulting diagrams contain only \({n \choose {\lfloor n/2 \rfloor}}\) intersection points, whereas a simple Venn diagram contains \(2^n-2\) intersection points. We show how to modify their construction to give symmetric Venn diagrams with asymptotically at least \(2^{n-1}\) intersection points, whence the name ``half-simple.''
scientific article; zbMATH DE number 2161277