Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Tuesday, October 27, 2009, 12:15 pm

Duration: This information is not available in the database

Location: OAT S15/S16/S17

Speaker: Torsten Mütze

The Search for Simple Symmetric Venn Diagrams

Venn diagrams are named after the British logician and philosopher John Venn (1834-1923) who introduced them as a tool in representing "propositions and reasonings". The Venn diagrams we usually encounter consist of exactly three circles and represent all 2^3=8 intersections of three sets. While it is straightforward to show that Venn diagrams can be drawn for any number n of sets (not using circles, though), the additional requirement that the resulting diagram has n-fold rotational symmetry (like the diagram consisting of three circles), makes the question of existence considerably more difficult. In this talk we discuss the breakthrough result of Griggs, Killian, Savage from 2004 who showed that there is a symmetric n-Venn diagram if and only if n is prime.

Talk mainly based on Jerrold Griggs, Charles E. Killian, and Carla D. Savage. Venn diagrams and symmetric chain decompositions in the Boolean lattice. Electron. J. Combin., 11:Research Paper 2, 30 pp. (electronic), 2004.

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