The Minimal sorting probabilities, and the champion pairs for Standard Young\

     Tableau of shape, [n, n, n, n], for n from 1 to, 12



                              By Shalosh B. Ekhad



The minimal sorting probability of Standard Young tableaux of shape,

    [2, 2, 2, 2],  but where one of the cells is in the first row is , 2/7,

    and in floating point, 0.2857142857,

    and this happens with the pairs of cells, {[[1, 2], [2, 1]]}

The minimal sorting probability of Standard Young tableaux of shape,

    [3, 3, 3, 3],  but where one of the cells is in the first row is , 1/11,

    and in floating point, 0.09090909091,

    and this happens with the pairs of cells, {[[1, 2], [2, 1]]}

The minimal sorting probability of Standard Young tableaux of shape,

    [4, 4, 4, 4],  but where one of the cells is in the first row is , 0,

    and in floating point, 0., and this happens with the pairs of cells, {

    [[1, 2], [2, 1]], [[1, 3], [3, 1]], [[1, 4], [2, 3]], [[1, 4], [3, 2]],

    [[1, 4], [4, 1]]}

The minimal sorting probability of Standard Young tableaux of shape,

    [5, 5, 5, 5],  but where one of the cells is in the first row is , 1/19,

    and in floating point, 0.05263157895,

    and this happens with the pairs of cells, {[[1, 2], [2, 1]]}

The minimal sorting probability of Standard Young tableaux of shape,

    [6, 6, 6, 6],  but where one of the cells is in the first row is , 2/23,

    and in floating point, 0.08695652174,

    and this happens with the pairs of cells, {[[1, 2], [2, 1]]}

The minimal sorting probability of Standard Young tableaux of shape,

                                                                       11881
    [7, 7, 7, 7],  but where one of the cells is in the first row is , ------,
                                                                       289731

    and in floating point, 0.04100700305,

    and this happens with the pairs of cells, {[[1, 6], [3, 3]]}

The minimal sorting probability of Standard Young tableaux of shape,

                                                                        88773
    [8, 8, 8, 8],  but where one of the cells is in the first row is , -------,
                                                                       1344005

    and in floating point, 0.06605109356,

    and this happens with the pairs of cells, {[[1, 5], [3, 2]]}

The minimal sorting probability of Standard Young tableaux of shape,

    [9, 9, 9, 9],  but where one of the cells is in the first row is ,

    224626067
    ----------, and in floating point, 0.08623935426,
    2604681690

    and this happens with the pairs of cells,

    {[[1, 7], [4, 2]], [[1, 8], [4, 3]]}

The minimal sorting probability of Standard Young tableaux of shape,

    [10, 10, 10, 10],  but where one of the cells is in the first row is ,

    196469528
    ----------, and in floating point, 0.02038631923,
    9637322253

    and this happens with the pairs of cells, {[[1, 7], [2, 5]]}

The minimal sorting probability of Standard Young tableaux of shape,

    [11, 11, 11, 11],  but where one of the cells is in the first row is ,

     23939431
    ----------, and in floating point, 0.02185012478,
    1095619876

    and this happens with the pairs of cells, {[[1, 6], [2, 4]]}

The minimal sorting probability of Standard Young tableaux of shape,

    [12, 12, 12, 12],  but where one of the cells is in the first row is ,

     300783304
    -----------, and in floating point, 0.004402001825,
    68328754959

    and this happens with the pairs of cells, {[[1, 7], [3, 3]]}



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