Enumerative combinatorics
Gray codes and efficient generation of combinatorial structures
Gray codes and efficient generation of combinatorial structures
Applied Combinatorial Mathematics
Applied Combinatorial Mathematics
Bond percolation critical probability bounds for three Archimedean lattices
Random Structures & Algorithms
Upper and Lower Bounds for the Kagomé Lattice Bond Percolation Critical Probability
Combinatorics, Probability and Computing
An Improved Upper Bound for the Hexagonal Lattice Site Percolation Critical Probability
Combinatorics, Probability and Computing
The Application of Non-Crossing Partitions to Improving Percolation Threshold Bounds
Combinatorics, Probability and Computing
Hi-index | 0.00 |
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 $p_c$. We demonstrate the symmetry reduction technique using bond percolation on the $(3,12^2)$ lattice, where we improve the bounds on $p_c$ from (0.738598,0.744900) to (0.739399,0.741757), a reduction of more than 62% in width, from 0.006302 to 0.002358.