The directed d-weight method is used to obtain the expansion of the mean-size series, S(p), for the simple acyclic hypercubic lattices, to order p 9 . The following expansion is also derived: p c (d)=1/d+1/2d 3 +1/d 4 +3/d 5 +21/2d 6 +479/12d 7 +O(d -8 ).
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J Blease (1977) studied this question.
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