Entropy, partitions and association schemes

In the previous talk, it was shown that entropy functions can be approximated by functions associated with uniform partitions (all parts have the same size). In this talk, we define orthogonality of partitions, and interpret orthogonality in terms of the entropy of the associated random variables. We explain how a sublattice of the partition lattice consisting of mutually orthogonal uniform partitions gives rise to an association scheme.