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

Date and Time: Thursday, November 09, 2006, 12:15 pm

Duration: This information is not available in the database

Location: OAT S15/S16/S17

Speaker: Uli Wagner

Set pairs (and, time permitting, quadrupels)

This will be, for the most part, an expository talk about (variants of) an extremal problem about finite sets, some results (key words ``Bollobás's Theorem'' and its ``skew version'') and some applications.

The focus will be on the proof methods.

Time permitting, we will also mention some recent generalizations.

If you are curious, the basic version of the problem is this: Suppose we are given some unknown number $t$ of pairs $(A_i,B_i)$ of finite sets, $1 \leq i \leq t$ with the following constraints:

0) $|A_i| \leq a$ and $|B_i| \leq b$ for all $i$, for some constants $a,b$;
1) $A_i \cap B_i = \emptyset$ for all $i$;
2) $A_i \cap B_j eq \emptyset$ for $i eq j$.

Bollobás showed that the number of pairs is at most $\binom{a+b}{a}$.

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