Fall 2003 8 Sm

A zipper has $N$ links each of which can be in two possible states - closed with energy $0$ and open with energy $\epsilon$. The zipper can only open from the left, i.e. a link $j$ can be open only if all the links to its left with indices $i$, $1 \le i < j$ are open.

1. Find the partition function of this system.
2. Find the average number of open links.

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