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, 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, n], are all the integers from, 2,  to , 9



                   as n goes to infinity, the distribution is



[[2., .5625000000], [3., .3281250000], [4., .9228515625e-1], [5., .1538085938e-\
1], [6., .1602172852e-2], [7., .1029968262e-3], [8., .3755092621e-5], [9., .\
5960464478e-7]]


 The limiting average, standard deviation up to the, 4,  -th scaled-moment are



[2.565784514, .7375154461, 1.230394748, 4.278575835]


                                 Here is a plot




  +H                                                                            
  + HH                                                                          
0.5   H                                                                         
  +    HH                                                                       
  +      H                                                                      
  +       H                                                                     
0.4       HH                                                                    
  +         H                                                                   
  +          HH                                                                 
0.3            H                                                                
  +             H                                                               
  +              HH                                                             
  +                H                                                            
0.2                 H                                                           
  +                  H                                                          
  +                   H                                                         
0.1                    H                                                        
  +                     HHHH                                                    
  +                         HHH                                                 
  +                            HHHHH                                            
  ++--+-+-+-+-+-+-+-+-+-+-+--+-+-+-+******************************************- 
0  2          3         4          5         6          7         8          9  




                 ---------------------------------------------



The occupants of cell, [1, 3], in a standard Young tableau of shape,

    [n, n, n, n, n, n, n, n], are all the integers from, 3,  to , 17



                   as n goes to infinity, the distribution is



[[3., .2343750000], [4., .3076171875], [5., .2409667969], [6., .1345825195], [7\
., .5716323853e-1], [8., .1901328564e-1], [9., .5021393299e-2], [10., .\
1057595015e-2], [11., .1770956442e-3], [12., .2332875738e-4], [13., .2369852155\
e-5], [14., .1794796844e-6], [15., .9559244063e-8], [16., .3200639753e-9], [17.
, .5080380561e-11]]


 The limiting average, standard deviation up to the, 4,  -th scaled-moment are



[4.556201763, 1.302683108, .8009344112, 3.468628950]


                                 Here is a plot




0.3      H                                                                      
  +    HH H                                                                     
  +   H    H                                                                    
  +  HH     H                                                                   
0.25H        HH                                                                 
  +H           H                                                                
  +            H                                                                
0.2             H                                                               
  +              H                                                              
  +              H                                                              
0.15              H                                                             
  +                H                                                            
  +                 H                                                           
  +                  H                                                          
0.1                   H                                                         
  +                    H                                                        
  +                     H                                                       
0.05                     HHH                                                    
  +                        HHH                                                  
  +                           HHHH                                              
  +--+-+-+-+-+-+-+-+-+-+-+-+--+-+-********************************************+ 
0        4         6          8        10        12         14        16        




                            -----------------------



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