CSU HAYWARD

DEPARTMENT OF MATHEMATICS AND

COMPUTER SCIENCE

COLLOQUIUM

Friday, May 16, 2003; Noon-1:00pm Sc N321

Speaker: Timothy M. Hsu, Department of Mathematics
San Jose State University

Partitioning the Boolean lattice into chains

Suppose that any given 20 members of the U.S. Senate form a different committee, as do every 40 and every 60. Can we arrange things so that every committee of 20 is overseen by a different committee of 40 whose membership contains the original 20? Can we do the same with committees of 40 and 60?

In this talk, we will discuss solutions to these and many similar problems in terms of partitions of the Boolean lattice (the partially ordered set of subsets of {1...n}) into chains (increasing sequences of nested subsets). We will also discuss conjectures of Furedi and Griggs as to which numerical distributions of chain sizes are possible in chain decompositions of the Boolean lattice, and we will discuss work by the speaker (joint with Mark Logan, Shahriar Shahriari, and Christopher Towse) towards these conjectures.

Essentially no background is required for this talk. It will be helpful, but not necessary, to have heard about binomial coefficients and partially ordered sets.

 

Please join us beforehand for Pizza!!!!