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I have completed the God's Algorithm calculations for the <U,R> group

in terms of W-conjugate classes (or really, in terms of representative

elements of W-conjugate classes), with the results below. In general,

the use of W-conjugates reduces the size of the problem by about

four times. However, I was surprised to see that for levels 1, 3, 5,

7, 9, and 11 the number of cubes was exactly four times larger than the

number of W-conjugate classes. My interpretation is that all cubes

in <U,R> at these levels are completely "asymmetric" with respect to

W. (They are somewhat symmetric with respect to M, of course.) However,

when level 13 turned out not to have a ratio of exactly 4 between cubes

and W-conjugate classes, I was rescued from the task of explaining why

all cubes at an odd distance from Start were asymmetric.

Level W-Conjugate Branching Total Branching Ratio Classes Factor Cubes Factor of Cubes to Classes

0 1 1 1 1 1 1 4 4 4 2 3 3 10 2.5 3.333 3 6 2 24 2.4 4 4 15 2.5 58 2.416 3.866 5 35 2.333 140 2.413 4 6 85 2.429 338 2.414 3.976 7 204 2.4 816 2.414 4 8 493 2.417 1,970 2.414 3.996 9 1,189 2.412 4,756 2.414 4 10 2,863 2.408 11,448 2.407 3.999 11 6,862 2.397 27,448 2.398 4 12 16,324 2.379 65,260 2.378 3.998 13 38,550 2.362 154,192 2.363 3.9997 14 90,192 2.340 360,692 2.339 3.9992 15 206,898 2.294 827,540 2.294 3.9997 16 462,893 2.237 1,851,345 2.237 3.9996 17 992,268 2.144 3,968,840 2.144 3.9998 18 1,973,209 1.989 7,891,990 1.988 3.9996 19 3,415,314 1.731 13,659,821 1.755 3.9996 20 4,618,491 1.352 18,471,682 1.352 3.9995 21 4,147,448 0.898 16,586,822 0.898 3.9993 22 2,010,449 0.485 8,039,455 0.485 3.9988 23 378,110 0.118 1,511,110 0.188 3.9965 24 11,894 0.031 47,351 0.031 3.9811 25 27 0.002 87 0.002 3.222

Total 18,373,824 73,483,200 3.9993 = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 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

If you don't have time to do it right today, what makes you think you are

going to have time to do it over again tomorrow?