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Irregular triangle read by rows: T(N,k) (0 <= k <= 4*N^2) are coefficients of exact wrapping probability for site percolation on a 2*N X 2*N 2D union jack lattice with periodic boundary conditions. This is for the probability that it wraps in both directionsdimensions.
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Irregular triangle read by rows: T(N,k) (0 <= k <= 4*N^2) are coefficients of exact wrapping probability for site percolation on a 2*N X 2*N 2D union jack lattice with periodic boundary conditions. This is for the probability that it wraps in both directions.
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Triangle begins:
0, 0, 2, 4, 1,
0, 0, 0, 0, 4, 48, 332, 1360, 3385, 5344, 5476, 3760, 1756, 560, 120, 16, 1,
0, 0, 0, 0, 0, 0, 6, 180, 3186, 38832, 343125, 2284920, 11812665, 48453246, 160204284, 432061500, 959302998, 1766890134, 2717497054, 3511031418, 3832283250, 3552960132, 2812344534, 1909555974, 1116592323, 563847696, 246161187, 92809456, 30100680, 8335404, 1947336, 376992, 58905, 7140, 630, 36, 1,
...
nonn,new,tabf
The DATA shows three rows of the triangle.
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qqq
Irregular triangle read by rows: T(N,k) (0 <= k <= 4*N^2) are coefficients of exact wrapping probability for site percolation on a 2*N X 2*N 2D union jack lattice with periodic boundary conditions.
The wrapping probability function is Sum_{k=0..4*N^2} T(N,k)*p^k*(1-p)^(4*N^2-k).
Stephan Mertens, <a href="https://wasd.urz.uni-magdeburg.de/mertens/research/percolation/">Percolation</a>
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