Abstract
The shape of percolation clusters in the directed percolation problem is studied within mean field theory. Low-density series expansions are obtained for bond and site problems on the square and triangular lattices. These are used to test a scaling formula for the pair connectedness which involves two lengths xi /sub ///( rho ) and xi perpendicular to ( rho ). Determination of the exponents nu /sub /// and nu perpendicular to for these lengths shows that all four problems are in the same universality class and the values support the hyperscaling relation beta =1/2(D nu perpendicular to + nu /sub ///- gamma ). An independent argument is given for this relation.
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