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The astute reader will have noticed that there *has* to be an error

in the table as it was originally posted. It is impossible for there

to be two distinct sequences of length 2, because there is only

one position unique up to M-conjugancy which is only one qturn from

Start. All of the lengths in the original table except for one were

short by one. I had two programs -- one to generate the sequences

to a file, and a second to analyze the sequences. The first program

did not write Start to the file, resulting in all the sequences

except one being one short. Here follows the correction.

(Incorrect) (Correct)

Operation Length Length of of Sequence SequenceF* 11 12 U* 10 11 L* 7 8 R* 3 4 D* 9 10 B* 2 2 !! F'* 7 8 U'* 10 11 L'* 4 5 R'* 6 7 D'* 7 8 B'* 2 3To take a little more interesting case, I tried i(F*D'*) ^ n. In this

case, there were 63 unique elements in the sequence, and then the

8-th through the 63-rd elements repeated. Hence, the final cycle had

56 elements rather than the 2 elements of the simpler cases.

Similarly, here there were 64 unique elements in the sequence, with the

9-th through the 64-th elements repeated. The final cycle still

(correctly) had 56 elements. The length of the final cycle has to be

even, of course, since qturns are odd.

= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 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

= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 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