The Limiting Distribution, as n goes to infinity, of the Occupant of Cell [1\ ,i] in a random Standard Young tableau of shape, [n, n, n, n, n, n, n], from i=2 to i=, 3 By Shalosh B. Ekhad --------------------------------------------- The occupants of cell, [1, 2], in a standard Young tableau of shape, [n, n, n, n, n, n, n], are all the integers from, 2, to , 8 as n goes to infinity, the distribution is [[2., .5714285714], [3., .3265306122], [4., .8746355685e-1], [5., .1332778009e-\ 1], [6., .1189980365e-2], [7., .5828475259e-4], [8., .1214265679e-5]] The limiting average, standard deviation up to the, 4, -th scaled-moment are [2.546499697, .7198704467, 1.224958649, 4.213008619] Here is a plot +H + HH 0.5 HH + H + HH + HH 0.4 H + HH + H + HH 0.3 H + HH + HH 0.2 H + HH + H + HH 0.1 HHH + HHHH + HHHHH ++--+-+--+-+--+-+--+-+-+--+-+--+-+--+-**************************************- 0 2 3 4 5 6 7 8 --------------------------------------------- The occupants of cell, [1, 3], in a standard Young tableau of shape, [n, n, n, n, n, n, n], are all the integers from, 3, to , 15 as n goes to infinity, the distribution is [[3., .2448979592], [4., .3148688047], [5., .2399000416], [6., .1285178795], [7\ ., .5147272213e-1], [8., .1580245355e-1], [9., .3749652416e-2], [10., .\ 6851432141e-3], [11., .9494637174e-4], [12., .9679735566e-5], [13., .6866413406\ e-6], [14., .3036169193e-7], [15., .6325352486e-9]] The limiting average, standard deviation up to the, 4, -th scaled-moment are [4.493273496, 1.263084164, .7930700555, 3.425276015] Here is a plot + H 0.3 HHHH + H H + HH HH 0.25H H + H + H 0.2 HH + H + H 0.15 H + H + H + H 0.1 H + HH + H 0.05 HHH + HHH + HHHHH +--+-+--+-+-+--+-+--+-+--+-+-+--+-+-****************************************+ 0 4 6 8 10 12 14 ----------------------- This took, 530.458, seconds.