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For site percolation, the partition function is 

where the summation is over all site percolation configurations g , s is the probability that a site is occupied, n$_{s}$ ( g ) is the number of occupied sites in g , and N is the total number of sites. The corresponding transfer matrix is defined in a way similar to that of the Potts model, but with a twist due to the presence of vacant sites and henceforth not all L end sites are occupied. Denote the number of end sites that are occupied by n = 0 , 1 $^{,}$· · · , L which can be distributed in ( L n ) different ways. Then there are a total of L 

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non-crossing partitions and the transfer matrix has the dimension d S L × d S $_{L}$. It is clear that we have d S L > d$_{L}$ . 

