Estimating the average, variance, and central scaled moments up to the, 4,

    for the number of occurences of the submatrix, [[1]],

     in row-echelon matrices of dimension k by , 2 k,

    matrices over GF(q) with q=, 2

                            for k from, 50,  to , 60

by simulating, 1000, times, using the amazing Calabi-Wilf algorithm for rando\
    mly generating a k-subspace of GF(q)^n



                              By Shalosh B. Ekhad



Below for the given dimension we repeat the simulation using, 1000,

    samples , three times to check that it is reliable

For , 50,  by , 100, row-echelon matrices over GF(q) with q=, 2, the average,\
     variance, and central scaled moments are estimated as follows, doing it\
     three times

[1297.216000, 650.470, .3185145667e-1, 2.810176673]


[1299.100000, 666.562, .1235202851, 2.933631690]


[1298.328000, 599.353, -.6439922901e-1, 3.008513961]


For , 51,  by , 102, row-echelon matrices over GF(q) with q=, 2, the average,\
     variance, and central scaled moments are estimated as follows, doing it\
     three times

[1350.187000, 662.184, .2192214478e-1, 2.713755537]


[1350.257000, 600.837, -.7261750423e-1, 2.822585762]


[1350.875000, 610.488, -.4212153331e-2, 2.859949045]


For , 52,  by , 104, row-echelon matrices over GF(q) with q=, 2, the average,\
     variance, and central scaled moments are estimated as follows, doing it\
     three times

[1403.406000, 656.107, -.1884325331e-1, 3.005697320]


[1402.663000, 658.168, .8116619043e-1, 2.869408785]


[1403.720000, 690.259, .1703210939, 3.131315703]


For , 53,  by , 106, row-echelon matrices over GF(q) with q=, 2, the average,\
     variance, and central scaled moments are estimated as follows, doing it\
     three times

[1456.475000, 695.158, -.1133499101, 3.025136699]


[1455.137000, 720.794, -.9552789285e-1, 3.116164542]


[1456.479000, 693.671, .1149454210, 2.936485918]


For , 54,  by , 108, row-echelon matrices over GF(q) with q=, 2, the average,\
     variance, and central scaled moments are estimated as follows, doing it\
     three times

[1511.249000, 668.901, -.5180947303e-1, 2.740713155]


[1509.316000, 757.602, .5265848470e-2, 2.910171299]


[1510.159000, 756.337, -.5446936223e-1, 2.997799811]


For , 55,  by , 110, row-echelon matrices over GF(q) with q=, 2, the average,\
     variance, and central scaled moments are estimated as follows, doing it\
     three times

[1566.320000, 769.347, .4742580489e-1, 2.694089240]


[1565.856000, 691.510, .5683619166e-1, 3.184111024]


[1566.504000, 734.736, .9249356272e-2, 3.208400278]


For , 56,  by , 112, row-echelon matrices over GF(q) with q=, 2, the average,\
     variance, and central scaled moments are estimated as follows, doing it\
     three times

[1622.613000, 778.411, .2855898861e-1, 2.723352653]


[1621.811000, 795.520, .3162359556e-1, 3.197425943]


[1621.772000, 782.920, -.1487328808, 3.003194742]


For , 57,  by , 114, row-echelon matrices over GF(q) with q=, 2, the average,\
     variance, and central scaled moments are estimated as follows, doing it\
     three times

[1680.197000, 844.886, -.8365201759e-1, 3.051650972]


[1679.498000, 816.120, -.8379419859e-1, 3.022717863]


[1680.056000, 752.497, .5641306847e-1, 3.376092937]


For , 58,  by , 116, row-echelon matrices over GF(q) with q=, 2, the average,\
     variance, and central scaled moments are estimated as follows, doing it\
     three times

[1740.415000, 879.647, .1228065695, 2.964041399]


[1739.275000, 851.620, -.6398321198e-1, 3.025255155]


[1738.814000, 943.164, .2515020785e-1, 2.667603748]


For , 59,  by , 118, row-echelon matrices over GF(q) with q=, 2, the average,\
     variance, and central scaled moments are estimated as follows, doing it\
     three times

[1797.062000, 876.056, -.8630382923e-1, 2.680148236]


[1798.294000, 896.801, -.1608790278, 3.213165161]


[1798.016000, 930.035, .1699765825e-1, 2.928067546]


For , 60,  by , 120, row-echelon matrices over GF(q) with q=, 2, the average,\
     variance, and central scaled moments are estimated as follows, doing it\
     three times

[1858.499000, 886.454, -.5049254197e-1, 2.738925023]


[1858.966000, 894.133, -.6712212350e-1, 3.126341172]


[1860.595000, 858.375, -.1116908100, 2.936623498]




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            This ends this article that took, 902.378, to generate