The notation for the sum operator is unclear. I’d advise writing the sum as i=k+2,...,k+n and using an i subscript inside the sum so it’s clearer what is being substituted where.
My initial inclination is to introduce Xn as the space of events on turn n, and define Xa:b:=b∏i=aXi and then you can express it as ∑σ∈Xk+2:k+nPn(xk+1,σ|x0...xk) .
The notation for the sum operator is unclear. I’d advise writing the sum as i=k+2,...,k+n and using an i subscript inside the sum so it’s clearer what is being substituted where.
The sum isn’t over i, though, it’s over all possible tuples of length n−1. Any ideas for how to make that more clear?
I find the current notation fine, but if you want to make it more explicit, you could do
∑xk+2∑xk+3⋯∑xk+nPn(…)
Thanks, I made this change to the post.
My initial inclination is to introduce Xn as the space of events on turn n, and define Xa:b:=b∏i=aXi and then you can express it as ∑σ∈Xk+2:k+nPn(xk+1,σ|x0...xk) .