The exact-counting method partially attractive chains

1 The exact-counting method (partially attractive chains) 

For a self-avoiding chain with N + 1 points (N links) on a square lattice or a simple cubic lattice, a contact can be defined as two points that are non-adjacent on the chain, and nearest neighbours on the lattice. Now let us consider the selfavoiding chains which have a given origin, N links, p contacts, and the same end-to-end vector r let ZN p r ) be the number of configurations of these chains. This number has been counted by W. Orr39 for N 8 on the square lattice and for N 6 on the simple cubic lattice. 

Moreover, three types of results have been obtained by counting such chains, and these are reviewed below. 

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