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$^{in Table VII. Explicitly, the thresholds for site percolation on (1}$× 1) : ( $^{n}$× n ) kagome-type subnet lattices, 1 ≤ n ≤ 6, in Table VII are as follows: 

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The threshold s$_{c}$ $^{= 1}$− 2 sin( π/ 18) for the n = 1 kagome lattice was first given in [35]. The threshold s$_{c}$ = 1 $_{/}$√$_{2 for}$ n = 2 has also been obtained by a “cell-to-cell” transformation in [36]. Here, the thresholds for 3 ≤ n ≤ 6 are new. 

We also computed s$_{c}$ and other critical properties numerically. The results are summa- rized in Table VII. Again, our numerical estimates of s$_{c}$ agree with the exact results up to 7 decimal places, and these models all belong to the two-dimensional q = 1 Potts model universality class. 

Finally, we comment on some numerical specifics. Since the number of non-crossing partitions for site percolation is much larger than that of the Potts model in both the magnetic and non-magnetic sector for a given circumference L , the maximum system size L = 12 that we reached is smaller. The largest dimension of arrays used to save values and positions of nonzero elements of the sparse matrices is d S ( m ) L =13 = 125481607, which requires about 43 gigabytes computer memory in the calculations. Corrections to scaling due to the leading irrelevant field is about − 1 . 8(1) for all lattices. 

