Let be the discrete space.
Compute for and for
I know that is defined to be for and for but I don't know exactly how to use that to solve the problem.
I assume that is the 'sphere' (that is an uncommon noation) of radius centered at . I think you're overthinking your problem. has a simple formulation. Think about fixing this one point then one can think (purely heuristically) as the situation being analgous to being the origin in and being the unit circle. With this in mind, is the solution clear?