Onody, R. N.; Neves, U. P. C. Series expansion of the directed percolation probability. (English) Zbl 0770.60091 J. Phys. A, Math. Gen. 25, No. 24, 6609-6615 (1992). Summary: Using a transfer-matrix technique we obtain extended series expansion of the percolation probability for the directed site percolation problem on the square lattice. Our approach reveals a previously unsuspected connection between this problem and the enumeration of the number of ways of dissecting a ball. We show that the method can also be used to determine a series expansion for the mean cluster size. An analysis based on Padé approximants gives estimates of the critical threshold and also of the critical exponent \(\beta\). Cited in 85 Documents MSC: 60K35 Interacting random processes; statistical mechanics type models; percolation theory 82B43 Percolation Keywords:percolation theory; transfer-matrix technique; percolation problem on the square lattice; Padé approximants PDFBibTeX XMLCite \textit{R. N. Onody} and \textit{U. P. C. Neves}, J. Phys. A, Math. Gen. 25, No. 24, 6609--6615 (1992; Zbl 0770.60091) Full Text: DOI Online Encyclopedia of Integer Sequences: a(n) = binomial(3*n,n)/(2*n+1) (enumerates ternary trees and also noncrossing trees). Percolation series for directed square lattice.