Co-author: Thomas Prellberg (Queen Mary, University of London)

Various kinds of paths on lattices are often used to model polymers. We describe some partially directed path models for which we find the exact generating functions, using instances of the `kernel method'. In particular, motivated by recent studies of DNA unzipping, we find and analyze the generating function for pairs of non-crossing partially directed paths with contact interactions. Although the expressions involving two-path problem are unweildy and tax the capacities of Maple and Mathematica, we are still able to gain an understanding of the singularities of the generating function which govern the behaviour of the model.