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

    for the number of occurences of the submatrix,

    [[1, 0, 2], [1, 0, 2], [1, 0, 1]],

     in row-echelon matrices of dimension k by , 3 k,

    matrices over GF(q) with q=, 3

                            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 , 150, row-echelon matrices over GF(q) with q=, 3, the average,\
     variance, and central scaled moments are estimated as follows, doing it\
     three times

[.2520000000, .2364960000, 1.801634382, 5.739153786]


[.2950000000, .3039750000, 1.935099072, 6.861635340]


[.2650000000, .2627750000, 1.926348838, 6.637078174]


For , 51,  by , 153, row-echelon matrices over GF(q) with q=, 3, the average,\
     variance, and central scaled moments are estimated as follows, doing it\
     three times

[.2510000000, .2539990000, 1.936748334, 6.201619357]


[.2800000000, .2656000000, 1.745637342, 5.688670344]


[.2630000000, .2578310000, 1.782628061, 5.320599011]


For , 52,  by , 156, row-echelon matrices over GF(q) with q=, 3, the average,\
     variance, and central scaled moments are estimated as follows, doing it\
     three times

[.2960000000, .3063840000, 1.792543512, 5.596250844]


[.2900000000, .2839000000, 1.788992795, 5.952345811]


[.2700000000, .2471000000, 1.727295614, 5.723450218]


For , 53,  by , 159, row-echelon matrices over GF(q) with q=, 3, the average,\
     variance, and central scaled moments are estimated as follows, doing it\
     three times

[.2620000000, .2473560000, 1.817504164, 6.064968279]


[.2950000000, .2979750000, 1.805159254, 5.894503890]


[.2800000000, .2796000000, 1.901887631, 6.618430990]


For , 54,  by , 162, row-echelon matrices over GF(q) with q=, 3, the average,\
     variance, and central scaled moments are estimated as follows, doing it\
     three times

[.3140000000, .2994040000, 1.690818376, 5.703123836]


[.3050000000, .3199750000, 1.866595322, 6.266359932]


[.3150000000, .3057750000, 1.672461366, 5.399025177]


For , 55,  by , 165, row-echelon matrices over GF(q) with q=, 3, the average,\
     variance, and central scaled moments are estimated as follows, doing it\
     three times

[.3000000000, .3040000000, 1.893636199, 6.977796053]


[.3070000000, .2987510000, 1.634595771, 4.923158386]


[.2960000000, .2743840000, 1.728365432, 6.056328555]


For , 56,  by , 168, row-echelon matrices over GF(q) with q=, 3, the average,\
     variance, and central scaled moments are estimated as follows, doing it\
     three times

[.3180000000, .3348760000, 1.962823314, 7.408095732]


[.3330000000, .3041110000, 1.456520952, 4.357582678]


[.3030000000, .2851910000, 1.680505597, 5.572943679]


For , 57,  by , 171, row-echelon matrices over GF(q) with q=, 3, the average,\
     variance, and central scaled moments are estimated as follows, doing it\
     three times

[.3320000000, .3397760000, 1.721674250, 5.615604637]


[.3290000000, .3307590000, 1.781730300, 6.420774383]


[.3490000000, .3671990000, 1.752872555, 5.854007237]


For , 58,  by , 174, row-echelon matrices over GF(q) with q=, 3, the average,\
     variance, and central scaled moments are estimated as follows, doing it\
     three times

[.3610000000, .3526790000, 1.594706107, 5.466586495]


[.3260000000, .3297240000, 1.990589944, 8.269090159]


[.3380000000, .3537560000, 1.799753976, 6.140880350]


For , 59,  by , 177, row-echelon matrices over GF(q) with q=, 3, the average,\
     variance, and central scaled moments are estimated as follows, doing it\
     three times

[.3710000000, .3493590000, 1.380661499, 4.002007538]


[.3540000000, .3506840000, 1.633416475, 5.401676302]


[.3560000000, .3572640000, 1.720146588, 6.183127190]


For , 60,  by , 180, row-echelon matrices over GF(q) with q=, 3, the average,\
     variance, and central scaled moments are estimated as follows, doing it\
     three times

[.3380000000, .3117560000, 1.489435043, 4.616897451]


[.3660000000, .3480440000, 1.523501885, 4.972584160]


[.3870000000, .4212310000, 1.938596197, 8.169841330]




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            This ends this article that took, 1737.881, to generate