Aa+Ua = Ab+Ub = F+Y = T+V = {Ga,Gb,Gc,Gd}

Xishem said:
if you apply a 3-cycle of edges and then a 3-cycle of corners that it can only produce a G perm
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Does this look like a G perm to you?
(R' U R' U' R' U' R' U R U R2) (R' F R' B2 R F' R' B2 R2)

Or this?
(R' U R' U' R' U' R' U R U R2) y2 (R' F R' B2 R F' R' B2 R2)

Athefre said:
Thom has a nice "Random Cubing Discussion" topic you could have posted this in without having people hatin on you.
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Ah yeah, that might've been a good place. I've noticed that thread but never really looked into it...
 
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TiLiMayor said:
So this is the side product of what?
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Side product of computing combinations of two PLLs. My results and program:
http://www.stefan-pochmann.info/misc/PLL_combinations.html - any other interesting things in this table?
http://www.stefan-pochmann.info/misc/PLL_combinations.txt

That in turn was my side product of attempting to count PLL attacks returning to solved.

Xishem said:
I never took into account the fact that Ja, Jb, Ra, and Rb perms also have AUFs where only one corner and one edge is solved. Are there any more?
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That's a good way to put it, I like that. And no, those are all.
 
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This *is* cool, and I think perfectly justified for a new thread. In fact, this should probably actually be in Puzzle Theory; it deserves to be there more so than the many threads people regularly post there (I regularly move them out; I don't even wanna know what a mess that subforum would be if I didn't moderate it constantly), although that wouldn't really free it from posts that detract from the discussion.

Ua and Aa I would have believed, but F+Y and T+V I wouldn't have suspected (but note that the latter two obviously imply each other's possibility by corner-edge duality).
 
Feel free to move it. By now with the discussion, including your very cool duality observation (*), I agree it's more theory than anything else. When I started it, I had no idea where it would go or whether it would get replies at all.

(*) In case someone doesn't know what that duality means: T is like Y, and V is like F, only with roles of edges and corners switched (describe how T looks like, replace "edge" with "corner" and "corner" with "edge", and you should have a description of Y). Or imagine you could also do eighth turns rather than just quarter turns, so you'd actually have edges and corners switch places in the cube.

Although, Lucas... while I can clearly see that duality between F+Y and V+T, I must admit I don't that easily see the duality between the G perms (yeah I just don't see it, they're too complicated... but I understand it must be there :))
 
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Arnaud showed me this. I asked why he used A-perm for 2-look PLL, he said he only did with the G-perms, because then he always knows which EPLL he'd have.

Edit: This was only related to G-perms, didn't know about the other two :p
 
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Stefan said:
I don't that easily see the duality between the G perms (yeah I just don't see it, they're too complicated... but I understand it must be there :))
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Had to paint it:
xe4avo.png


Now I see Ga and Gc are duals, as are Gb and Gd.
 
I learnt my 2LOLL by using T-Perm+U-Perm for basically everything.
Next I learnt H Perm (as it's so easy to memo), and Z Perm (again, easy to memo).
Then Y-Perm (gives you Y, and the 2 N-Perms).

A-Perms I learnt quite late. x R' U' R always confused the heck out of me, I'd have to stop and think for 5 seconds and mis-execute. In fact, I've been "properly" speed-cubing for 5 months now and only in the last 2 weeks am I really starting to nail my A-perms fast and consistent.

Even then I still sort-of have to think "Block on the left side, headlights on top-or-bottom, rotate-cube-toward-headlights, move-r-face-the-other-diretion, fingertrick.."

As a result I'm either going to find BH-commutators very, very easy or very, very hard.
 
Stefan said:
Now I see Ga and Gc are duals, as are Gb and Gd.
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Yeah, that's exactly the image I had in mind, thanks for explaining things to everybody. If you draw each arrow the same (instead of different colors), it becomes more obvious: a G-perm is two three-cycles in opposite directions, fully interleaved (none leaves a hole in the other).
T/Y/V/F are a bit funny because they're all self-inverses and self-mirrors, though their combinations are asymmetric – making twice the possible algs.

So, the question is: Is there an intuitive reason the two 3-cycles produced by T+V (or F+Y) should interleave completely?
 
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Tim Major said:
Arnaud showed me this. I asked why he used A-perm for 2-look PLL, he said he only did with the G-perms, because then he always knows which EPLL he'd have.
Edit: This was only related to G-perms, didn't know about the other two :p
Click to expand...

Isn't it quite common to use A-perm for 2-look PLL?
I already realised A-perming a G-perm always results in U-perm but didn't notice the a-a and b-b relation.
I also used to AUF the G-perm with headlights in the back.

Seems I can skip that AUF now.

Cool stuff!

Idea: got no cube with me so I cannot check right now:
Could you start with the G in such an orientation that you can cancel the R2 at the end of A with the R2 beginning of U?
 
toastman said:
A-Perms I learnt quite late. x R' U' R always confused the heck out of me, I'd have to stop and think for 5 seconds and mis-execute. Even then I still sort-of have to think "Block on the left side, headlights on top-or-bottom, rotate-cube-toward-headlights, move-r-face-the-other-diretion, fingertrick.."
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Try to think of x R’ U R’ as l U R’
I actually think along the lines of “pulling U R’ ‘over’ the cube”
 
Lucas Garron said:
If you draw each arrow the same (instead of different colors), it becomes more obvious:
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Bawww... but I did that on purpose... note the colors do *not* stick to the type of piece but to which cycle it is relative to the non-moving pieces. Pink is the cycle counterclockwise-next from the dots, black the clockwise-next. For Ga and Gb, pink is edges. For Gc and Gd, pink is corners. For me that makes it *easier* to see the relation.

Lucas Garron said:
So, the question is: Is there an intuitive reason the two U-perms produced by T+V and F+Y should interleave?
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Two U-perms? Are you comparing T+V and F+Y? I don't get it.

Cubenovice said:
Idea: got no cube with me so I cannot check right now:
Could you start with the G in such an orientation that you can cancel the R2 at the end of A with the R2 beginning of U?
Click to expand...

http://alg.garron.us/
http://thearufam.brinkster.net/cube/wrapplet.asp
[noparse][/noparse]
 
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Lucas Garron said:
So, the question is: Is there an intuitive reason the two 3-cycles produced by T+V (or F+Y) should interleave completely?
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Well I view the defining trait of an interleaved corner and edge cycle as the 1x1x2 block that is preserved. Working with F+Y(proving T+V as well is obviously not needed), two of the angles are obvious, as a portion of the 1x1x3 block is preserved. For Fperm(bar in front) y Yperm(standard) and the y2 one, there only one corner that moves to the position opposite its origin, and one edge as well. If you think about the N-perms, it's easy to see how this will always result in the formation of a 1x1x2 block.
 
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