We obtain two new partition properties from AD. The first result (joint
with A. Apter and B. Löwe)
is that for every inaccessible Suslin cardinal $\kappa$ we have the
polarized partition property
(kappa,kappa^+,kappa^++) -> (kappa,kappa^+,kappa^++)^(kappa,kappa,kappa)
This was used to obtain the consistency relative to ZF of the possible
patters of cofinalities of the first three
uncountable cardinals.
The second result pins down the exact partition
properties of the regular
cardinals below the projective ordinals.