Yes, all pmsrw3 has said is the way I meant it: Instead of a set you can take it as a vector and ask for the transition probability between the two "state-vectors". Though I doubt that linear algebra is going to help, since formulating as this language we need something like a transition matrix...
I am dealing with the following interesting combinatorics problem, several reformulations of which haven't help me solve the problem:
Suppose we have a circular arrangement with M spots and we want to distribute N tokens over these spots such that there are token numbers n_m that respect...