|
|
|
|
Is there a matching for n=8 between levels 3 and 4? True Level set 3 [[1, 1, 6], [1, 2, 5], [1, 3, 4], [2, 2, 4], [2, 3, 3]] Level set 4 [[1, 1, 1, 5], [1, 1, 2, 4], [1, 1, 3, 3], [1, 2, 2, 3], [2, 2, 2, 2]] The list of edges between level set 3 and level set 4 [[0, 0], [0, 1], [0, 2], [1, 0], [1, 1], [1, 3], [2, 1], [2, 2], [2, 3], [3, 1], [3, 3], [3, 4], [4, 2], [4, 3]] The number of times each edge appeared in a random walk [100, 0, 0, 0, 100, 0, 0, 73, 27, 0, 0, 100, 27, 73] For n=8, the matching data from our random walk is ********************************n = 8 ******************************** *********k = 1 to k = 2 ********* [8] ( 4 ) to [1, 7] ( 1 ) : 0.380 [8] ( 4 ) to [2, 6] ( 1 ) : 0.240 [8] ( 4 ) to [3, 5] ( 1 ) : 0.360 [8] ( 4 ) to [4, 4] ( 1 ) : 0.0200 *********k = 2 to k = 3 ********* [1, 7] ( 3 ) to [1, 1, 6] ( 2 ) : 0.650 [1, 7] ( 3 ) to [1, 2, 5] ( 3 ) : 0.350 [1, 7] ( 3 ) to [1, 3, 4] ( 3 ) : 0.000 [2, 6] ( 4 ) to [1, 1, 6] ( 2 ) : 0.000 [2, 6] ( 4 ) to [1, 2, 5] ( 3 ) : 0.000 [2, 6] ( 4 ) to [2, 2, 4] ( 2 ) : 0.790 [2, 6] ( 4 ) to [2, 3, 3] ( 2 ) : 0.210 [3, 5] ( 3 ) to [1, 2, 5] ( 3 ) : 0.000 [3, 5] ( 3 ) to [1, 3, 4] ( 3 ) : 0.210 [3, 5] ( 3 ) to [2, 3, 3] ( 2 ) : 0.790 [4, 4] ( 2 ) to [1, 3, 4] ( 3 ) : 0.790 [4, 4] ( 2 ) to [2, 2, 4] ( 2 ) : 0.210 *********k = 3 to k = 4 ********* [1, 1, 6] ( 3 ) to [1, 1, 1, 5] ( 2 ) : 0.540 [1, 1, 6] ( 3 ) to [1, 1, 2, 4] ( 4 ) : 0.420 [1, 1, 6] ( 3 ) to [1, 1, 3, 3] ( 3 ) : 0.0400 [1, 2, 5] ( 3 ) to [1, 1, 1, 5] ( 2 ) : 0.460 [1, 2, 5] ( 3 ) to [1, 1, 2, 4] ( 4 ) : 0.300 [1, 2, 5] ( 3 ) to [1, 2, 2, 3] ( 4 ) : 0.240 [1, 3, 4] ( 3 ) to [1, 1, 2, 4] ( 4 ) : 0.280 [1, 3, 4] ( 3 ) to [1, 1, 3, 3] ( 3 ) : 0.380 [1, 3, 4] ( 3 ) to [1, 2, 2, 3] ( 4 ) : 0.340 [2, 2, 4] ( 3 ) to [1, 1, 2, 4] ( 4 ) : 0.000 [2, 2, 4] ( 3 ) to [1, 2, 2, 3] ( 4 ) : 0.000 [2, 2, 4] ( 3 ) to [2, 2, 2, 2] ( 1 ) : 1.00 [2, 3, 3] ( 2 ) to [1, 1, 3, 3] ( 3 ) : 0.580 [2, 3, 3] ( 2 ) to [1, 2, 2, 3] ( 4 ) : 0.420 *********k = 4 to k = 5 ********* [1, 1, 1, 5] ( 2 ) to [1, 1, 1, 1, 4] ( 2 ) : 0.670 [1, 1, 1, 5] ( 2 ) to [1, 1, 1, 2, 3] ( 4 ) : 0.330 [1, 1, 2, 4] ( 3 ) to [1, 1, 1, 1, 4] ( 2 ) : 0.330 [1, 1, 2, 4] ( 3 ) to [1, 1, 1, 2, 3] ( 4 ) : 0.0600 [1, 1, 2, 4] ( 3 ) to [1, 1, 2, 2, 2] ( 3 ) : 0.190 [1, 1, 3, 3] ( 1 ) to [1, 1, 1, 2, 3] ( 4 ) : 0.610 [1, 2, 2, 3] ( 2 ) to [1, 1, 1, 2, 3] ( 4 ) : 0.000 [1, 2, 2, 3] ( 2 ) to [1, 1, 2, 2, 2] ( 3 ) : 0.290 [2, 2, 2, 2] ( 1 ) to [1, 1, 2, 2, 2] ( 3 ) : 0.520 *********k = 5 to k = 6 ********* [1, 1, 1, 1, 4] ( 2 ) to [1, 1, 1, 1, 1, 3] ( 2 ) : 0.000 [1, 1, 1, 1, 4] ( 2 ) to [1, 1, 1, 1, 2, 2] ( 3 ) : 0.0100 [1, 1, 1, 2, 3] ( 2 ) to [1, 1, 1, 1, 1, 3] ( 2 ) : 1.00 [1, 1, 1, 2, 3] ( 2 ) to [1, 1, 1, 1, 2, 2] ( 3 ) : 0.000 [1, 1, 2, 2, 2] ( 1 ) to [1, 1, 1, 1, 2, 2] ( 3 ) : 0.990 *********k = 6 to k = 7 ********* [1, 1, 1, 1, 1, 3] ( 1 ) to [1, 1, 1, 1, 1, 1, 2] ( 2 ) : 0.660 [1, 1, 1, 1, 2, 2] ( 1 ) to [1, 1, 1, 1, 1, 1, 2] ( 2 ) : 0.340 *********k = 7 to k = 8 ********* [1, 1, 1, 1, 1, 1, 2] ( 1 ) to [1, 1, 1, 1, 1, 1, 1, 1] ( 1 ) : 1.00 Is there a matching for n=8 between levels 3 and 4? True Level set 3 [[1, 1, 6], [1, 2, 5], [1, 3, 4], [2, 2, 4], [2, 3, 3]] Level set 4 [[1, 1, 1, 5], [1, 1, 2, 4], [1, 1, 3, 3], [1, 2, 2, 3], [2, 2, 2, 2]] The list of edges between level set 3 and level set 4 [[0, 0], [0, 1], [0, 2], [1, 0], [1, 1], [1, 3], [2, 1], [2, 2], [2, 3], [3, 1], [3, 3], [3, 4], [4, 2], [4, 3]] The number of times each edge appeared in a random walk [100, 0, 0, 0, 100, 0, 0, 73, 27, 0, 0, 100, 27, 73] For n=8, the matching data from our random walk is ********************************n = 8 ******************************** *********k = 1 to k = 2 ********* [8] ( 4 ) to [1, 7] ( 1 ) : 0.380 [8] ( 4 ) to [2, 6] ( 1 ) : 0.240 [8] ( 4 ) to [3, 5] ( 1 ) : 0.360 [8] ( 4 ) to [4, 4] ( 1 ) : 0.0200 *********k = 2 to k = 3 ********* [1, 7] ( 3 ) to [1, 1, 6] ( 2 ) : 0.650 [1, 7] ( 3 ) to [1, 2, 5] ( 3 ) : 0.350 [1, 7] ( 3 ) to [1, 3, 4] ( 3 ) : 0.000 [2, 6] ( 4 ) to [1, 1, 6] ( 2 ) : 0.000 [2, 6] ( 4 ) to [1, 2, 5] ( 3 ) : 0.000 [2, 6] ( 4 ) to [2, 2, 4] ( 2 ) : 0.790 [2, 6] ( 4 ) to [2, 3, 3] ( 2 ) : 0.210 [3, 5] ( 3 ) to [1, 2, 5] ( 3 ) : 0.000 [3, 5] ( 3 ) to [1, 3, 4] ( 3 ) : 0.210 [3, 5] ( 3 ) to [2, 3, 3] ( 2 ) : 0.790 [4, 4] ( 2 ) to [1, 3, 4] ( 3 ) : 0.790 [4, 4] ( 2 ) to [2, 2, 4] ( 2 ) : 0.210 *********k = 3 to k = 4 ********* [1, 1, 6] ( 3 ) to [1, 1, 1, 5] ( 2 ) : 0.540 [1, 1, 6] ( 3 ) to [1, 1, 2, 4] ( 4 ) : 0.420 [1, 1, 6] ( 3 ) to [1, 1, 3, 3] ( 3 ) : 0.0400 [1, 2, 5] ( 3 ) to [1, 1, 1, 5] ( 2 ) : 0.460 [1, 2, 5] ( 3 ) to [1, 1, 2, 4] ( 4 ) : 0.300 [1, 2, 5] ( 3 ) to [1, 2, 2, 3] ( 4 ) : 0.240 [1, 3, 4] ( 3 ) to [1, 1, 2, 4] ( 4 ) : 0.280 [1, 3, 4] ( 3 ) to [1, 1, 3, 3] ( 3 ) : 0.380 [1, 3, 4] ( 3 ) to [1, 2, 2, 3] ( 4 ) : 0.340 [2, 2, 4] ( 3 ) to [1, 1, 2, 4] ( 4 ) : 0.000 [2, 2, 4] ( 3 ) to [1, 2, 2, 3] ( 4 ) : 0.000 [2, 2, 4] ( 3 ) to [2, 2, 2, 2] ( 1 ) : 1.00 [2, 3, 3] ( 2 ) to [1, 1, 3, 3] ( 3 ) : 0.580 [2, 3, 3] ( 2 ) to [1, 2, 2, 3] ( 4 ) : 0.420 *********k = 4 to k = 5 ********* [1, 1, 1, 5] ( 2 ) to [1, 1, 1, 1, 4] ( 2 ) : 0.670 [1, 1, 1, 5] ( 2 ) to [1, 1, 1, 2, 3] ( 4 ) : 0.330 [1, 1, 2, 4] ( 3 ) to [1, 1, 1, 1, 4] ( 2 ) : 0.330 [1, 1, 2, 4] ( 3 ) to [1, 1, 1, 2, 3] ( 4 ) : 0.0600 [1, 1, 2, 4] ( 3 ) to [1, 1, 2, 2, 2] ( 3 ) : 0.190 [1, 1, 3, 3] ( 1 ) to [1, 1, 1, 2, 3] ( 4 ) : 0.610 [1, 2, 2, 3] ( 2 ) to [1, 1, 1, 2, 3] ( 4 ) : 0.000 [1, 2, 2, 3] ( 2 ) to [1, 1, 2, 2, 2] ( 3 ) : 0.290 [2, 2, 2, 2] ( 1 ) to [1, 1, 2, 2, 2] ( 3 ) : 0.520 *********k = 5 to k = 6 ********* [1, 1, 1, 1, 4] ( 2 ) to [1, 1, 1, 1, 1, 3] ( 2 ) : 0.000 [1, 1, 1, 1, 4] ( 2 ) to [1, 1, 1, 1, 2, 2] ( 3 ) : 0.0100 [1, 1, 1, 2, 3] ( 2 ) to [1, 1, 1, 1, 1, 3] ( 2 ) : 1.00 [1, 1, 1, 2, 3] ( 2 ) to [1, 1, 1, 1, 2, 2] ( 3 ) : 0.000 [1, 1, 2, 2, 2] ( 1 ) to [1, 1, 1, 1, 2, 2] ( 3 ) : 0.990 *********k = 6 to k = 7 ********* [1, 1, 1, 1, 1, 3] ( 1 ) to [1, 1, 1, 1, 1, 1, 2] ( 2 ) : 0.660 [1, 1, 1, 1, 2, 2] ( 1 ) to [1, 1, 1, 1, 1, 1, 2] ( 2 ) : 0.340 *********k = 7 to k = 8 ********* [1, 1, 1, 1, 1, 1, 2] ( 1 ) to [1, 1, 1, 1, 1, 1, 1, 1] ( 1 ) : 1.00 |
|
|