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],
as n goes to infinity for i from 2 to, 16
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
[-.2500000000]
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
[-.8750000000]
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
[-.9921875000]
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
[.3750000000, -.5585937500]
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
[-.5625000000, -.9711914062]
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
[-.9516601562, -.9995727539]
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
[.7265625000, .4882812500e-2, -.6988983154]
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
[-.1586914062, -.8474731445, -.9899063110]
The cut off is at j=, 1
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
[-.8536605835, -.9951133728, -.9999449253]
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
[.8906250000, .4493408203, -.2279281616, -.7775691748]
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
[.2215576172, -.6031265259, -.9331836700, -.9955733716]
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
[-.6916699409, -.9763718843, -.9991178215, -.9999888130]
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
[.9589843750, .7256774902, .2210413218, -.3842742220, -.8270631481]
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
[.5174484253, -.2784743309, -.7912320048, -.9662123220, -.9977604431]
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
[-.4790973356, -.9281271277, -.9943753127, -.9997775576, -.9999969754]
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
[.9853515625, .8738403320, .5541627407, .3988571186e-1, -.4948451448, -.8606198\
697]
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
[.7198128700, .5882309377e-1, -.5587753663, -.8804509981, -.9811187809, -.99874\
80598]
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
[-.2403236853, -.8371775120, -.9784422539, -.9982919769, -.9999300241, -.999999\
0036]
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
[.9949645996, .9455108643, .7649301291, .3952118484, -.1038218591, -.5762752719
, -.8846134596]
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
[.8458195478, .3547862666, -.2676476412, -.7184207032, -.9268642606, -.98863903\
21, -.9992464762]
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
[-.5484390722e-3, -.6990094341, -.9406232287, -.9923054546, -.9993853421, -.999\
9742080, -.9999996205]
The cut off is at j=, 1
---------------------------------------------
The limits of the sorting probabilities of the cell, [1, 9], vs. those in the,
2, -th row from j=1 to j=, 8, as n goes to infinity, are as follows
[.9983215332, .9776277542, .8840546012, .6482240148, .2542385573, -.2189692421,
-.6382109932, -.9024689377]
The cut off is at j=, 6
The limits of the sorting probabilities of the cell, [1, 9], vs. those in the,
3, -th row from j=1 to j=, 8, as n goes to infinity, are as follows
[.9188619582, .5842477479, .3482973675e-1, -.4867139515, -.8130337112, -.952848\
4682, -.9927625355, -.9995198421]
The cut off is at j=, 4
The limits of the sorting probabilities of the cell, [1, 9], vs. those in the,
4, -th row from j=1 to j=, 8, as n goes to infinity, are as follows
[.2206926201, -.5198134332, -.8703524856, -.9755835807, -.9968771832, -.9997490\
738, -.9999892867, -.9999998385]
The cut off is at j=, 2
---------------------------------------------
The limits of the sorting probabilities of the cell, [1, 10], vs. those in the,
2, -th row from j=1 to j=, 9, as n goes to infinity, are as follows
[.9994544983, .9911897182, .9458826510, .8085669489, .5329292834, .1313379231,
-.3124107033, -.6865705148, -.9161785177]
The cut off is at j=, 7
The limits of the sorting probabilities of the cell, [1, 10], vs. those in the,
3, -th row from j=1 to j=, 9, as n goes to infinity, are as follows
[.9588754029, .7460512025, .3084843887, -.2143026350, -.6331855128, -.871466556\
0, -.9682807378, -.9951750473, -.9996798178]
The cut off is at j=, 4
The limits of the sorting probabilities of the cell, [1, 10], vs. those in the,
4, -th row from j=1 to j=, 9, as n goes to infinity, are as follows
[.4117518240, -.3138098155, -.7614931222, -.9396091427, -.9889600700, -.9986004\
482, -.9998870443, -.9999951136, -.9999999249]
The cut off is at j=, 2
---------------------------------------------
The limits of the sorting probabilities of the cell, [1, 11], vs. those in the,
2, -th row from j=1 to j=, 10, as n goes to infinity, are as follows
[.9998264313, .9966498017, .9758871710, .9015257411, .7258112301, .4236607812,
.2477818705e-1, -.3892176457, -.7251575098, -.9269731482]
The cut off is at j=, 8
The limits of the sorting probabilities of the cell, [1, 11], vs. those in the,
3, -th row from j=1 to j=, 10, as n goes to infinity, are as follows
[.9798126205, .8518850313, .5309389545, .6239045372e-1, -.4006901290, -.7324564\
456, -.9089434955, -.9779001576, -.9966619083, -.9997784354]
The cut off is at j=, 5
The limits of the sorting probabilities of the cell, [1, 11], vs. those in the,
4, -th row from j=1 to j=, 10, as n goes to infinity, are as follows
[.5681910983, -.9840226154e-1, -.6149074674, -.8759714370, -.9699013685, -.9946\
107397, -.9993211247, -.9999450195, -.9999975970, -.9999999625]
The cut off is at j=, 2
---------------------------------------------
The limits of the sorting probabilities of the cell, [1, 12], vs. those in the,
2, -th row from j=1 to j=, 11, as n goes to infinity, are as follows
[.9999457598, .9987634569, .9896737253, .9517270203, .8477618927, .6406655847,
.3223862231, -.6761778122e-1, -.4531206652, -.7565130402, -.9356506270]
The cut off is at j=, 8
The limits of the sorting probabilities of the cell, [1, 12], vs. those in the,
3, -th row from j=1 to j=, 11, as n goes to infinity, are as follows
[.9903596572, .9170060978, .6969672159, .3131828519, -.1421731714, -.5386711261
, -.8010179253, -.9337971325, -.9841424105, -.9976182719, -.9998418809]
The cut off is at j=, 5
The limits of the sorting probabilities of the cell, [1, 12], vs. those in the,
4, -th row from j=1 to j=, 11, as n goes to infinity, are as follows
[.6907994878, .1102961727, -.4382755640, -.7792750017, -.9325033495, -.98410844\
92, -.9971978180, -.9996487005, -.9999714700, -.9999987427, -.9999999801]
The cut off is at j=, 3
---------------------------------------------
The limits of the sorting probabilities of the cell, [1, 13], vs. those in the,
2, -th row from j=1 to j=, 12, as n goes to infinity, are as follows
[.9999833107, .9995551761, .9957267039, .9773029577, .9194640691, .7878064993,
.5563151117, .2296480835, -.1479527923, -.5068822512, -.7823908869, -.942748503\
9]
The cut off is at j=, 9
The limits of the sorting probabilities of the cell, [1, 13], vs. those in the,
3, -th row from j=1 to j=, 12, as n goes to infinity, are as follows
[.9955052658, .9550944371, .8125165888, .5206279142, .1133014744, -.3068925964,
-.6410153284, -.8493204250, -.9507701016, -.9883331176, -.9982557866, -.9998841\
823]
The cut off is at j=, 6
The limits of the sorting probabilities of the cell, [1, 13], vs. those in the,
4, -th row from j=1 to j=, 12, as n goes to infinity, are as follows
[.7834391532, .3002259006, -.2437651045, -.6491369561, -.8699521074, -.96170233\
24, -.9911853924, -.9984639082, -.9998081435, -.9999843833, -.9999993070, -.999\
9999889]
The cut off is at j=, 3
---------------------------------------------
The limits of the sorting probabilities of the cell, [1, 14], vs. those in the,
2, -th row from j=1 to j=, 13, as n goes to infinity, are as follows
[.9999949336, .9998435271, .9982837121, .9897106384, .9591634568, .8805369681,
.7243522816, .4746969160, .1452612016, -.2180842274, -.5525710127, -.8040355482
, -.9486408588]
The cut off is at j=, 10
The limits of the sorting probabilities of the cell, [1, 14], vs. those in the,
3, -th row from j=1 to j=, 13, as n goes to infinity, are as follows
[.9979479089, .9764382976, .8883779561, .6797769295, .3428475666, -.6110432680e\
-1, -.4377748901, -.7174980048, -.8840118658, -.9626636396, -.9912294588, -.998\
6938433, -.9999132545]
The cut off is at j=, 6
The limits of the sorting probabilities of the cell, [1, 14], vs. those in the,
4, -th row from j=1 to j=, 13, as n goes to infinity, are as follows
[.8512931729, .4642835271, -.4490515349e-1, -.4904932478, -.7779163649, -.92116\
80405, -.9774405728, -.9948986151, -.9991192684, -.9998903262, -.9999910557, -.\
9999996008, -.9999999936]
The cut off is at j=, 3
---------------------------------------------
The limits of the sorting probabilities of the cell, [1, 15], vs. those in the,
2, -th row from j=1 to j=, 14, as n goes to infinity, are as follows
[.9999984801, .9999460326, .9993286257, .9954833012, .9800546213, .9355262151,
.8365552178, .6594635225, .3968992584, .6869646933e-1, -.2795913461, -.59175567\
93, -.8223515177, -.9535952137]
The cut off is at j=, 11
The limits of the sorting probabilities of the cell, [1, 15], vs. those in the,
3, -th row from j=1 to j=, 14, as n goes to infinity, are as follows
[.9990803286, .9879687072, .9357791411, .7944043181, .5334943988, .1753317973,
-.2092074774, -.5413707474, -.7752229258, -.9093811496, -.9711891269, -.9932821\
397, -.9990028010, -.9999337625]
The cut off is at j=, 7
The limits of the sorting probabilities of the cell, [1, 15], vs. those in the,
4, -th row from j=1 to j=, 14, as n goes to infinity, are as follows
[.8996823845, .5998754114, .1461326752, -.3123431929, -.6559997749, -.856963984\
2, -.9508925088, -.9862601871, -.9969366580, -.9994751306, -.9999348002, -.9999\
946741, -.9999997612, -.9999999961]
The cut off is at j=, 4
---------------------------------------------
The limits of the sorting probabilities of the cell, [1, 16], vs. those in the,
2, -th row from j=1 to j=, 15, as n goes to infinity, are as follows
[.9999995488, .9999817093, .9997434561, .9980733215, .9905778516, .9664901016,
.9070410405, .7890285383, .5946386250, .3234573220, -.7128181804e-3, -.33379428\
50, -.6256412029, -.8380100093, -.9578074130]
The cut off is at j=, 11
The limits of the sorting probabilities of the cell, [1, 16], vs. those in the,
3, -th row from j=1 to j=, 15, as n goes to infinity, are as follows
[.9995945836, .9940031886, .9641642223, .8726417593, .6816843225, .3851090368,
.2363839666e-1, -.3331875501, -.6234672325, -.8192626789, -.9282446230, -.97742\
43667, -.9947691641, -.9992257041, -.9999485608]
The cut off is at j=, 8
The limits of the sorting probabilities of the cell, [1, 16], vs. those in the,
4, -th row from j=1 to j=, 15, as n goes to infinity, are as follows
[.9333983202, .7077887366, .3202154832, -.1256458195, -.5080361623, -.765799433\
6, -.9061462663, -.9686214140, -.9913790958, -.9981000990, -.9996765176, -.9999\
598988, -.9999967197, -.9999998523, -.9999999976]
The cut off is at j=, 4
-------------------------
This ends this article that took, 7009.257, seconds to produce
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This took, 7009.257, seconds.