Background Material: Entropy of partial orders
Gwenaël Joret, (Université Libre de Bruxelles)

G. Simonyi, 
Perfect Graphs and Graph Entropy. An Updated Survey,
Chapter 13 in: Perfect Graphs (Jorge Ramirez-Alfonsin, Bruce Reed eds.), 
John Wiley and Sons, 2001, 293-328. 
[pdf]

J. Kahn and J. H. Kim. 
Entropy and sorting. 
J. Comput. Syst. Sci., 51(3):390-399, 1995. 
[pdf]

R. P. Stanley. 
Two poset polytopes. 
Discrete Comput. Geom., 1:9-23, 1986. 
[link]

J. Cardinal, S. Fiorini, G. Joret, R. M. Jungers, and J. I. Munro.
Sorting under partial information (without the ellipsoid algorithm).
To appear in Combinatorica
[pdf]