The Limiting Sorting Probabilities of The entries in the first row vs. thos\ e not related to it in lower rows in a random Standard Young tableau of shape, [n, n, n, n, n, n, n], as n goes to infinity for i from 2 to, 4 By Shalosh B. Ekhad --------------------------------------------- The limits of the sorting probabilities of the cell, [1, 2], vs. those in the, 2, -th row from j=1 to j=, 1, as n goes to infinity, are as follows [-.1428571429] The cut off is at j=, 1 The limits of the sorting probabilities of the cell, [1, 2], vs. those in the, 3, -th row from j=1 to j=, 1, as n goes to infinity, are as follows [-.7959183673] The cut off is at j=, 1 The limits of the sorting probabilities of the cell, [1, 2], vs. those in the, 4, -th row from j=1 to j=, 1, as n goes to infinity, are as follows [-.9708454810] The cut off is at j=, 1 The limits of the sorting probabilities of the cell, [1, 2], vs. those in the, 5, -th row from j=1 to j=, 1, as n goes to infinity, are as follows [-.9975010412] The cut off is at j=, 1 The limits of the sorting probabilities of the cell, [1, 2], vs. those in the, 6, -th row from j=1 to j=, 1, as n goes to infinity, are as follows [-.9998810020] The cut off is at j=, 1 The limits of the sorting probabilities of the cell, [1, 2], vs. those in the, 7, -th row from j=1 to j=, 1, as n goes to infinity, are as follows [-.9999975715] The cut off is at j=, 1 --------------------------------------------- The limits of the sorting probabilities of the cell, [1, 3], vs. those in the, 2, -th row from j=1 to j=, 2, as n goes to infinity, are as follows [.5102040816, -.4535003030] The cut off is at j=, 2 The limits of the sorting probabilities of the cell, [1, 3], vs. those in the, 3, -th row from j=1 to j=, 2, as n goes to infinity, are as follows [-.3294460641, -.9381302891] The cut off is at j=, 1 The limits of the sorting probabilities of the cell, [1, 3], vs. those in the, 4, -th row from j=1 to j=, 2, as n goes to infinity, are as follows [-.8313797822, -.9968660263] The cut off is at j=, 1 The limits of the sorting probabilities of the cell, [1, 3], vs. those in the, 5, -th row from j=1 to j=, 2, as n goes to infinity, are as follows [-.9762173924, -.9999310190] The cut off is at j=, 1 The limits of the sorting probabilities of the cell, [1, 3], vs. those in the, 6, -th row from j=1 to j=, 2, as n goes to infinity, are as follows [-.9982401078, -.9999994230] The cut off is at j=, 1 The limits of the sorting probabilities of the cell, [1, 3], vs. those in the, 7, -th row from j=1 to j=, 2, as n goes to infinity, are as follows [-.9999466837, -.9999999987] The cut off is at j=, 1 --------------------------------------------- The limits of the sorting probabilities of the cell, [1, 4], vs. those in the, 2, -th row from j=1 to j=, 3, as n goes to infinity, are as follows [.8250728863, .1839458118, -.6063716275] The cut off is at j=, 3 The limits of the sorting probabilities of the cell, [1, 4], vs. those in the, 3, -th row from j=1 to j=, 3, as n goes to infinity, are as follows [.1831974772, -.6981527114, -.9741084739] The cut off is at j=, 2 The limits of the sorting probabilities of the cell, [1, 4], vs. those in the, 4, -th row from j=1 to j=, 3, as n goes to infinity, are as follows [-.5430305400, -.9676100740, -.9993879436] The cut off is at j=, 1 The limits of the sorting probabilities of the cell, [1, 4], vs. those in the, 5, -th row from j=1 to j=, 3, as n goes to infinity, are as follows [-.9026002664, -.9985862050, -.9999950598] The cut off is at j=, 1 The limits of the sorting probabilities of the cell, [1, 4], vs. those in the, 6, -th row from j=1 to j=, 3, as n goes to infinity, are as follows [-.9894699620, -.9999778846, -.9999999885] The cut off is at j=, 1 The limits of the sorting probabilities of the cell, [1, 4], vs. those in the, 7, -th row from j=1 to j=, 3, as n goes to infinity, are as follows [-.9995494578, -.9999999138, -1.000000000] The cut off is at j=, 1 ------------------------- This ends this article that took, 16404.297, seconds to produce ----------------------- This took, 16404.297, seconds.