= Single-block DNA zipper partition function
{title2=$q$}
A homogeneous <DNA> zipper permitting exactly one contiguous paired block of length $j\ge1$ has $N-j+1$ block positions and weight $\kappa s^{j-1}$. Consequently its <partition function> is $q=\kappa\sum_{j=1}^N(N-j+1)s^{j-1}=\kappa[s^{N+1}-(N+1)s+N]/(s-1)^2$. The removable value at $s=1$ is $\kappa N(N+1)/2$. At large s, $q\sim\kappa s^{N-1}$. Including an unpaired state gives the full partition function $1+q$; the large-s limit is not uniform in arbitrarily small initiation weight.
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