L 1 2 3 2 L+1 L 1 3 2 1 L−1 L L+1 L 1 2 L−1 1 L+1 L L−1 L−2 (a) (b) (d) (e) (c) FIG. 8: Construction of the transfer matrix for kagome-type subnet lattices. The procedure consists of several steps each corresponding to a sparse transfer matrix. 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 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$_{L}$ . Z = ∑ g s n s ( g $^{)}$(1 − s ) N − n s ( g ) = 1 , (15) d S L = L ∑ n $_{=0}$( L n ) d$_{n}$ (16) 11