Speaker: Prof. Prasad Tetali

Affiliation: MSRI, Berkeley, on leave from
             School of Mathematics & College of Computing
             Georgia Tech., Atlanta

Title: An Entropy Technique in Combinatorics

An entropy lemma due to J. Shearer from 1986 has played a key role
in providing tight estimates for a number of combinatorial enumeration
problems in the recent few years. The speaker will cover basic facts
about entropy and will introduce and illustrate a technique which 
has been employed effectively in the papers listed below. These include 
results on estimating the number of antichains and linear extensions in the
Boolean lattice, and also the number of (proper) $k$-colorings of a regular 
bipartite graph, for fixed $k$. 

3. The number of linear extensions of the Boolean lattice:
   G. Brightwell and P. Tetali,  Order  Vol. 20 (2003), 333-345 (2004).

2. On weighted graph homomorphisms: D. Galvin and P. Tetali
   DIMACS-AMS Special Volume Vol. 63 (2004), 97-104.

1. Entropy, independent sets and antichains: a new approach to 
   Dedekind's problem. Proc. Amer. Math. Soc. 130 (2002), no. 2, 371--378.

(The talk is intended to be accessible to a broad audience with little
background on the topics mentioned.)