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], as n goes to infinity for i from 2 to, 8 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 [-.2000000000] 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 [-.8400000000] 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 [-.9840000000] 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 [-.9993600000] 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 [.4400000000, -.5116800000] 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 [-.4560000000, -.9580672000] 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 [-.9040000000, -.9987814400] 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 [-.9937075200, -.9999913984] 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 [.7760000000, .8723200000e-1, -.6589142016] 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 [.5440000000e-2, -.7859737600, -.9841010483] 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 [-.7236172800, -.9866834944, -.9998100079] 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 [-.9725560545, -.9998124950, -.9999996064] 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 [.9193600000, .5313152000, -.1449232998, -.7438305497] 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 [.3993932800, -.4687842304, -.8986621911, -.9926474075] 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 [-.4534566380, -.9395258515, -.9971059601, -.9999563791] 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 [-.9221913961, -.9984730783, -.9999865192, -.9999999651] The cut off is at j=, 1 --------------------------------------------- The limits of the sorting probabilities of the cell, [1, 6], vs. those in the, 2, -th row from j=1 to j=, 5, as n goes to infinity, are as follows [.9731200000, .7865072640, .3185491026, -.3061522757, -.7984023748] The cut off is at j=, 4 The limits of the sorting probabilities of the cell, [1, 6], vs. those in the, 3, -th row from j=1 to j=, 5, as n goes to infinity, are as follows [.6717518848, -.8314098893e-1, -.6981026108, -.9459079304, -.9961366301] The cut off is at j=, 2 The limits of the sorting probabilities of the cell, [1, 6], vs. those in the, 4, -th row from j=1 to j=, 5, as n goes to infinity, are as follows [-.1401007312, -.8293425385, -.9827049509, -.9991755361, -.9999871631] The cut off is at j=, 1 The limits of the sorting probabilities of the cell, [1, 6], vs. those in the, 5, -th row from j=1 to j=, 5, as n goes to infinity, are as follows [-.8318922587, -.9928495407, -.9998401616, -.9999983929, -.9999999953] The cut off is at j=, 1 --------------------------------------------- The limits of the sorting probabilities of the cell, [1, 7], vs. those in the, 2, -th row from j=1 to j=, 6, as n goes to infinity, are as follows [.9915520000, .9112732672, .6390903504, .1426989755, -.4231417231, -.8360168257 ] The cut off is at j=, 5 The limits of the sorting probabilities of the cell, [1, 7], vs. those in the, 3, -th row from j=1 to j=, 6, as n goes to infinity, are as follows [.8345505833, .2775727065, -.3950364473, -.8171981996, -.9685509799, -.99777866\ 50] The cut off is at j=, 3 The limits of the sorting probabilities of the cell, [1, 7], vs. those in the, 4, -th row from j=1 to j=, 6, as n goes to infinity, are as follows [.1643778548, -.6442968634, -.9385457842, -.9940573361, -.9997173166, -.9999955\ 022] The cut off is at j=, 2 The limits of the sorting probabilities of the cell, [1, 7], vs. those in the, 5, -th row from j=1 to j=, 6, as n goes to infinity, are as follows [-.6987519713, -.9767126495, -.9989718306, -.9999753791, -.9999997321, -.999999\ 9991] The cut off is at j=, 1 --------------------------------------------- The limits of the sorting probabilities of the cell, [1, 8], vs. those in the, 2, -th row from j=1 to j=, 7, as n goes to infinity, are as follows [.9974656000, .9657027584, .8258772701, .4955975979, -.1260481713e-2, -.5110527\ 604, -.8632656511] The cut off is at j=, 5 The limits of the sorting probabilities of the cell, [1, 8], vs. those in the, 3, -th row from j=1 to j=, 7, as n goes to infinity, are as follows [.9219613860, .5586565712, -.4963975570e-1, -.5911797662, -.8833706216, -.98049\ 83501, -.9986337964] The cut off is at j=, 3 The limits of the sorting probabilities of the cell, [1, 8], vs. those in the, 4, -th row from j=1 to j=, 7, as n goes to infinity, are as follows [.4239263996, -.3979251651, -.8443291639, -.9751159592, -.9976626708, -.9998889\ 519, -.9999982054] The cut off is at j=, 2 The limits of the sorting probabilities of the cell, [1, 8], vs. those in the, 5, -th row from j=1 to j=, 7, as n goes to infinity, are as follows [-.5286382170, -.9413811540, -.9956070754, -.9998019248, -.9999950487, -.999999\ 9432, -.9999999998] The cut off is at j=, 1 ------------------------- This ends this article that took, 5289.994, seconds to produce ----------------------- This took, 5289.994, seconds.