Easily rearranging arguments without using FA
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September 16 2015
|It's common knowledge that the clusterswaps the second and third position. How do you construct a minimal cluster to create an arbitrary place structure.|
|I think any method is still too difficult to work for real-time human processing|
|... permutation groups|
|I'm assuming we'll be using a buffer position to break into new "orbits"?|
The reason we reverse is because the order of application is reversed for orbits and .
|What about (3 4 2) ?|
|Also equivalent. It's the fact that we can rotate orbits like that that we use to prove (2) :)|
That would be «te se ve te», of course.
|This seems exactly the same as rubik's cube BLD cycles, except having to go backwards because of.|
|So we start with:|
1 2 3 4 5
2 1 3 4 5 (se)
3 1 2 4 5 (te)
4 1 2 3 5 (ve)
1 4 2 3 5 (se)
This technique allows us to arbitrarily re-arrange the last 4 places.
|Well this is way easier than doing each step in one's mind.|
Only problem is that backwards SE is confusing
|Rotations work on any length of SE right?|
|I think this is more of a for-fun thing. I'm not sure it's practical.|
|It's not practical, in that using multiple SE in a row is ugly and rare, but it's more practical than memorizing all the SE* combinations and their resulting place structures|
|Kind of. They have to be of form r_1 ... r_n r_1 and ∀ 1 ≤ i, j ≤ n; i ≠ j <=> r_i ≠ r_j|
I.e. you can't rotate nor .
|Can I rotate te se te or se te se? What would be a five-tuple that I can rotate?|