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We have derived long series expansions of the percolation probability forsite, bond and site-bond percolation on the directed triangular lattice. Forthe bond problem we have extended the series from order 12 to 51 and for thesite problem from order 12 to 35. For the site-bond problem, which has not beenstudied before, we have derived the series to order 32. Our estimates of thecritical exponent $\beta$ are in full agreement with results for similarproblems on the square lattice, confirming expectations of universality. Forthe critical probability and exponent we find in the site case: $q_c =0.4043528 \pm 0.10$ and $\beta = 0.27645 \pm 0.00010$; in the bond case:$q_c = 0.52198\pm 0.00001$ and $\beta = 0.2769\pm 0.0010$; and in the site-bondcase: $q_c = 0.264173 \pm 0.3$ and $\beta = 0.2766 \pm 0.0003$. Inaddition we have obtained accurate estimates for the critical amplitudes. Inall cases we find that the leading correction to scaling term is analytic,i.e., the confluent exponent $\Delta = 1$.Comment: 26 pages, LaTeX. To appear in J. Phys.

Series expansions of the percolation probability on the directed triangular lattice