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Enumerating 2D percolation series by the finite-lattice method: Theory. (English) Zbl 0849.05003
Summary: This paper describes a transfer-matrix algorithm for enumeration of series of interest in percolation on the square lattice. It allows efficient generation of both low-temperature and high-temperature expansions, as well as the combinatorially interesting enumeration of undirected animals by area or perimeter, with moments of the other property.
MSC:
05A15Exact enumeration problems, generating functions
82B43Percolation (equilibrium statistical mechanics)
60K35Interacting random processes; statistical mechanics type models; percolation theory