Archives

Distance  Positions  Positions   Positions
 from                 reduced     reduced
 Start                  by           by
                      Symmetry    Symmetry
                                    and
                                 Anti-Symmetry

  0             1          1          1
  1            12          1          1
  2           114          5          5
  3           924         24         17
  4          6539        149         96
  5         39528        850        469
  6        199926       4257       2289
  7        806136      16937       8768
  8       2761740      57848      29603
  9       8656152     180787      91688
 10      22334112     466220     235710
 11      32420448     676786     342593
 12      18780864     392342     199610
 13       2166720      45600      23818
 14          6624        163        110

Total    88179840    1841970     934778

As I have written before, my programs have seldom worked with positions. They have nearly always worked with representative elements of M-conjugate classes. In the table above, the summary of representative elements is labeled "Positions Reduced by Symmetry". The goal of this approach is to obtain a 48 times speedup in processing time, and also to obtain a 48 times reduction in storage requirements.