Exact enumeration of parallel walks on directed lattices
- 7 September 1993
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 26 (17) , L863-L869
- https://doi.org/10.1088/0305-4470/26/17/019
Abstract
Mutually avoiding pairs of parallel walks on a number of d-dimensional lattices are mapped onto undirected random walks which return to the origin on a projected (d-1)-dimensional lattice. Generating functions for the number of such pairs of a given length are thus expressed in terms of standard Green's functions. Directed lattices considered include the directed hypercubic and body-centred hypercubic. The generating function for a directed triangular lattice is also obtained. This work is a generalization of known results for the square lattice.Keywords
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