Mark Longridge's antislice results are as follows:

                  arrangements           arrangements
Moves Deep   (2q or anti-slice moves)   (4q or double anti-slice moves)

0                   1                     1
1                   6                     9
2                  27                    51
3                 120                   265
4                 423                   864
5               1,098                 1,785
6               1,770                 2,017
7               1,650                 1,008
8                 851                   144
9                 198
                -----                 -----
                6,144                 6,144

We now have the following M-conjugacy results (2q moves only,
still working on 4q moves).

Level              Positions             Local
                                        Maxima

0                    1                    0
1                    1                    0
2                    3                    0
3                   10                    0
4                   37                    0
5                   93                    1
6                  166                    2
7                  147                    7
8                   89                   12
9                   21                   21
                  ----
                   568

The level 5 local maximum is (U'D')(FB)(FB)(UD)(L'R'). The position is
not its own inverse, but we can use as an inverse (U'D')(FB)(FB)(UD)(LR).
Hence, (U'D')(FB)(FB)(UD) forms a nice "middle" of the sequence. In
fact, the (U'D')(FB)(FB)(UD) position in some ways seems more
interesting than the local maximum itself. Does it already have
a name?

I have not verified if the length of the local maximum is 10q in G,
nor if it is a local maximum in G.

 = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
Robert G. Bryan (Jerry Bryan)                        (304) 293-5192
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