Date: Fri, 14 Apr 95 21:12:53 -0400
From: Jerry Bryan <BRYAN@wvnvm.wvnet.edu >
~~~ Subject: Re: Repetitive Application of Elements of Q*

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       Sequence
```
```F*                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             3
```

To 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
``` = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =