k-comparable.k-n

Here are the statistics on the number of pairs u<_kw in S_n
given as an array in (k,rank), where rank := l(w)-l(u):
All Calculations took place on Toronto's Coxeter, an SGI machine

S4:
   \  rank
    \ r  1    2    3   4
  k  \-------------------     
   1 |  26   18    6  
   2 |  34   29   12   4
   3 |  26   18    6  

k-comparable.maple took  .236  seconds


S5:
    \  rank
     \  r  1     2     3    4   5   6
   k  \------------------------------- 
    1 |  154   142   84   24   
    2 |  224   269  200  110  42  12
    3 |  224   269  200  110  42  12
    4 |  154   142   84   24   
					
k-comparable.maple took  1.532  sec.


S6:
  \  rank
   \  r  1     2     3     4     5    6    7    8   9
 k  \------------------------------------------------------  
 1  | 1044  1160   930   480   120   
 2  | 1608  2386  2414  1860  1094  544  192   48 
 3  | 1788  2866  3107  2584  1720  948  408  144  36
 4  | 1608  2386  2414  1860  1094  544  192   48 
 5  | 1044  1160   930   480   120   

k-comparable.maple took  39.790   seconds


S7:
  \  rank
   \  r   1    2     3     4     5     6     7     8    9   10    11   12
 k  \------------------------------------------------------------------------  
  1 |  8028 10208  9990  7080  3240   720 
  2 | 12816 22074 27312 26476 20348 13264  7250  3300 1080   240 
  3 | 15084 29208 39991 42840 37576 28232 18162 10196 4896  1980  648  144
  4 | 15084 29208 39991 42840 37576 28232 18162 10196 4896  1980  648  144
  5 | 12816 22074 27312 26476 20348 13264  7250  3300 1080   240 
  6 |  8028 10208  9990  7080  3240   720 

k-comparable.maple took   834.744  seconds


S8:

  \ rank 
   \ r   1       2       3       4        5      6        7      8 
 k  \----------------------------------------------------------------  
  1 |  69264   97720  110544   96600   61320   25200    5040 
  2 | 113328  218568  312936  358764  334372  265116  182044  110218 
  3 | 138192  307012  495420  635028  674374  618196  498364  358882 
  4 | 146256  338844  567146  751559  827252  788174  661156  497364 
  5 | 138192  307012  495420  635028  674374  618196  498364  358882 
  6 | 113328  218568  312936  358764  334372  265116  182044  110218 
  7 |  69264   97720  110544   96600   61320   25200    5040 

  \  rank 
   \  r   9       10      11     12    13     14    15   16
 k  \-----------------------------------------------------------  
  2 |  56220   23640    7200   1440 
  3 | 230928  133158   68508  31020  11820  3600   720 
  4 | 337040  206952  114752  57124  24816  9456  2880  576
  5 | 230928  133158   68508  31020  11820  3600   720 
  6 |  56220   23640    7200   1440 

	k-comparable.maple took 49217.223 seconds