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         




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



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