A zipper has N links every link has a state in which it is closed with energy 0 and a state in which it is open with energy 0 We require that the zipper only unzip from one side (say from the left) and that the link can only open if all links to the left of it (1,2,..., n-1) are previously open. This model is occasionally used for DNA molecules.
a) Find the partition function
b) Compute the average number of open links and show that for low temperatures ??<< ∈ is independent of N.