Date: Mon, 22 May 95 17:48:42 -0400
From: michael reid <mreid@ptc.com >
Subject: AntiSlice Under M-conjugacy (and a problem with slice)

jerry writes (about the antislice group)

```The level 5 local maximum is (U'D')(FB)(FB)(UD)(L'R').
```
```[ ... ]
```

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

this is exactly what i tried to explain in my recent posts: the latter
statement follows from the former. and yes, its length is indeed 10q.
it's pretty easy to find maneuvers which end in each quarter turn:

```(F'B') (UUDD) (FB) (RL)    =
(U'D') (FFBB) (UD) (R'L')  =
(R'L') (U'D') (FFBB) (UD)  =
(R'L') (UD) (FFBB) (U'D')  =
(RL) (F'B') (UUDD) (FB)    =
(RL) (FB) (UUDD) (F'B').
```

We have the following M-conjugacy results for 4q moves. Strong
and weak local maxima are defined according to my preference.

it seems like jerry's terminology is more reasonable, so i'll stop
using mine. jerry's figures

```Level       Positions     Strong      Weak        Total
Local Max   Local Max   Local Max
```
```0              1           0           0           0
1              2           0           0           0
2              5           0           0           0
3             25           0           1           1
4             75           0           2           2
5            152           0          19          19
6            184           1          35          36
7            108           0          46          46
8             16           0          16          16
----
568
```

beg the obvious question: what is that strong local maximum,
which is unique up to symmetry?

mike