Abstract
We show that symmetry, represented by a graph's automorphism group, can be used to greatly reduce the computational work for the substitution method. This allows application of the substitution method over larger regions of the problem lattices, resulting in tighter bounds on the percolation threshold from (0.738598,0.744900) to (0.739399,0.741757), a reduction of more than 62% in width, from 0.006302 to 0.002358.
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