Date: Monday, November 1, 2004 Time: 4:00 p.m. Room: LIT 339

Abstract: Let [n] = {1, 2, ...,n} and consider families F of its subsets: F subset 2^[n]. A typical question is to ask the maximum size of F satisfying a certain condition. We will start from the theorem of Sperner (1928) which answers this question under the condition that there is no inclusion among the members of F. We will show some old and new results of this type, and some more complicated problems when the number of members is fixed and a "transformed" family has to be optimized. An example is the so-called shadow problem. The easier methods and some open questions will be exhibited too.

 ^* Professor Katona is the director of the Mathematics Institute of the Hungarian Academy of Sciences. His most famous results include the Kruskal-Katona theorem, and a simple proof of the Erdos-Ko-Rado Theorem. He has 117 publications in MathSciNet.

This featured lecture is being arranged in connection with the Mathematics Department's Special Year in Number Theory and Combinatorics For more information see the website:
http://qseries.org/specialyears/2004-5/.