De Finetti has defined in 1938 the concept of partial exchangeability as a weaker form of exchangeability in order to deal with situations in which the symmetry among all observations is not desirable.
That's what I know and mere googling does not help this time because I've just found a bunch of papers that are a bit too advanced for me.
My questions are: what is the formal definition of partial exchangeability and does the results holding with exchangeability still holding (e.g. De Finetti representation theorem)? Can you give me an example of a situation in which partial exchangeability is meaningful?