2006/09/04 by WILLIAM D. MAY, William D. May, JOHN C. WIERMAN +1 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Stochastic processes and statistical mechanics #Surface Chemistry and Catalysis #Theoretical and Computational Physics
paper · doi:10.1017/s0963548306007905
openalex publication_date 2006/09/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/11
We describe how non-crossing partitions arise in substitution method calculations. By using efficient algorithms for computing non-crossing partitions we are able to substantially reduce the computational effort, which enables us to compute improved bounds on the percolation thresholds for three percolation models. For the Kagomé bond model we improve bounds from 0.5182 ≤ p c ≤ 0.5335 to 0.522197 ≤ p c ≤ 0.526873, improving the range from 0.0153 to 0.004676. For the (3, 12 2 ) bond model we improve bounds from 0.7393 ≤ p c ≤ 0.7418 to 0.739773 ≤ p c ≤ 0.741125, improving the range from 0.0025 to 0.001352. We also improve the upper bound for the hexagonal site model, from 0.794717 to 0.743359.