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], as n goes to infinity for i from 2 to, 5 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 [-.1666666667] 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 [-.8148148148] 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 [-.9768518519] 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 [-.9984567901] 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 [-.9999571331] 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 [.4814814815, -.4783736283] 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 [-.3827160494, -.9471585569] 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 [-.8640260631, -.9978368071] 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 [-.9851092948, -.9999678498] 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 [-.9993593774, -.9999998787] 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 [.8055555556, .1433172820, -.6292572238] 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 [.1105967078, -.7371839754, -.9788030182] 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 [-.6219457305, -.9771054041, -.9996158339] 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 [-.9373558864, -.9993235848, -.9999980858] 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 [-.9960699780, -.9999952245, -.9999999983] The cut off is at j=, 1 --------------------------------------------- The limits of the sorting probabilities of the cell, [1, 5], vs. those in the, 2, -th row from j=1 to j=, 4, as n goes to infinity, are as follows [.9351851852, .5839390273, -.8568993977e-1, -.7179889488] The cut off is at j=, 3 The limits of the sorting probabilities of the cell, [1, 5], vs. those in the, 3, -th row from j=1 to j=, 4, as n goes to infinity, are as follows [.5032531245, -.3691207516, -.8685501061, -.9897966777] The cut off is at j=, 2 The limits of the sorting probabilities of the cell, [1, 5], vs. those in the, 4, -th row from j=1 to j=, 4, as n goes to infinity, are as follows [-.2842033867, -.9005691672, -.9943559571, -.9999035150] The cut off is at j=, 1 The limits of the sorting probabilities of the cell, [1, 5], vs. those in the, 5, -th row from j=1 to j=, 4, as n goes to infinity, are as follows [-.8310097537, -.9947697716, -.9999372376, -.9999997980] The cut off is at j=, 1 The limits of the sorting probabilities of the cell, [1, 5], vs. those in the, 6, -th row from j=1 to j=, 4, as n goes to infinity, are as follows [-.9851767814, -.9999362848, -.9999998805, -.9999999999] The cut off is at j=, 1 ------------------------- This ends this article that took, 4621.390, seconds to produce ----------------------- This took, 4621.390, seconds.