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On 07/10/95 at 16:20:29 Jerry Bryan said:

The local maximum unique up to M-conjugacy is the 6-H position

(see Symmetry and Local Maxima). I do not yet have a process

for the 6-H, but I should be able to have one soon.

I can now give one way to do it as (UD)(RR)(LL)(UD). It seems too

simple once you chase it down. Note that this is *not* the 6-H

position when you apply the process to the whole cube; you have

to omit the corners for this process to yield the 6-H. Nonetheless,

the pattern is a nice one when the process is applied to the whole

cube, one that looks familiar, although I cannot place it. It is

*almost* what I described as the "interesting" part of three of the

10q local maxima on the whole cube, but the "interesting" part of

the 10q local maxima is (U'D')(RR)(LL)(UD) instead.

It might be noted that the length of this position

is also 8q on an edges-only-without-centers cube (see my note

of 8 Dec 1993 22:41:38). I did not actually provide a process

for the without-centers case, but the same process

works for the 6-H edges-only with or without centers for this position.

Such is not always true. I have talked about it before, but many

minimal processes for without-center cubes induce an invisible

rotation which becomes visible when the Face centers are included.

This is probably as good a time as any to correct an old error, pointed

out to me by Dan Hoey. The length of a position without centers is

the minimum taken over C of the length of the same position with

centers -- that is, the minimum of the respective lengths of the

same position rotated 24 different ways. For searches without centers

I store representatives of the form Y=Repr{m'Xmc}. At one point,

I said |Y|=min{|Yc|}. This is certainly not true. Y is just one

of the {Yc}, and it is totally arbitrary which one it is. The difficulty

is really a notational one. It is the length of Y without centers

which is min{|Yc|}, not the length of Y itself (with centers). But

I don't have a good way to say "Y without centers" or especially to

say "length of Y without centers".

But in any case, the most interesting cases to me are the ones where

the length without centers matches the length with centers, so that the

minimal process for the without centers case does not induce an

invisible rotation. The position at hand is such a case.

Finally, the position is in the anti-slice group (i.e.,

(UD)(RL)(RL)(UD)), so the position is a local maximum in the

anti-slice edges only group with a length 4a.

= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = Robert G. Bryan (Jerry Bryan) (304) 293-5192 Associate Director, WVNET (304) 293-5540 fax 837 Chestnut Ridge Road BRYAN@WVNVM Morgantown, WV 26505 BRYAN@WVNVM.WVNET.EDU