[next] [prev] [up] Date: Tue, 16 Dec 80 18:41:00 -0500 (EST)
[next] [prev] [up] From: James Saxe <James.Saxe@CMU-10A >
~~~ ~~~ [up] Subject: 16 qtw algs for CC and H patterns

In his note of 4 Nov 1980, 00:23 EST, David Plummer gives a
20 qtw algorithm for the Christman cross based on the following tool
for producing a 4-cross pattern:
4+ = FB UUDD F'B' R'L' UUDD RL UUDD
This can be reduced to 16 moves as follows:
4+ = FB UD LLRR UD FB UUDD
Consequently, Plummer's 16 qtw Christman cross algorithm, conceptually
B' 4+ B, can be reduced to
B' [FB UD LLRR UD FB UUDD] B
= F UD LLRR UD FB UUDD B (16 qtw).
[Note: There is another 4-cross pattern besides the above, namely
LLRR F LLRR FB LLRR B' LLRR F'B'.]

The H pattern which Dan Hoey and I described in our earlier
message (14 Dec 1980, 19:16 EST, Sec. 4) can be achieved in 16 qtw
as follows:
FF LL DD FF BB DD RR FF
This makes it the second proven example of a local maximum which is
not a global maximum. Of course this applies equally to the second
H pattern which is Pons Asinorum away from the above. I count these
two as only one example since they are M-conjugates.
--Jim Saxe


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