Additivity of the dp-rank
  The main result of this article is sub-additivity of the dp-rank. We also show that the study of theories of finite dp-rank can not be reduced to the study of its dp-minimal types, and discuss the possible relations between dp-rank and VC-density. 
Itay Kaplan, Alf Onshuus, and Alexander Usvyatsov
math.LO math.CO