From:

Subject:

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 Max0 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