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Half-simple symmetric Venn diagrams. (English) Zbl 1060.05002

Summary: A Venn diagram is simple if at most two curves intersect at any given point. A recent paper of 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.”

MSC:

05A10 Factorials, binomial coefficients, combinatorial functions
06A07 Combinatorics of partially ordered sets

Citations:

Zbl 1034.06001
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