Non-Commutative Gaussian Elimination and Rubik's Cube

[Lucas Garron]

Whee!
http://www.math.toronto.edu/drorbn/Talks/Mathcamp-0907/index.html
http://www.math.toronto.edu/drorbn/Talks/Mathcamp-0907/NCGE.pdf

Spoiler

 

[MiloD]

WTF...WTF.........WTF

btw, really cool and relevant to my interests.

 

[qqwref]

It sounds like a kinda cool idea, but I'm no longer good at following along on heavily condensed math language. Do you have a more thorough explanation of the NCGE algorithm and the "feeding" idea?

 

[LewisJ]

Heh, I was just looking at this two or three days ago. Itai Bar-Natan was at MC10, although I don't recall seeing him with a cube at any point. Perhaps Raku or Devin actually attended the class in 09, we both went in the wrong year...

 

[FMC]

Can someone explain the method?

 

[oll+phase+sync]

While the math itself seems somehow logic step by step I have difficulties to see the big picture.
Does this article state more then, it is solvable - plus giving an general program skeleton?

If I'm right each step of the methode solves at least one stricker ==> maximum of 54 steps

But one Sticker can not be solved alone, if there are more stickers an the same cubie ==> maximum of 28 steps

In the result are some numbers does that mean every cube can be solved in 3 steps ?

It would be cool if the lenght of the steps were limited, when measured in turns of the cube.

I feel like the first Step is maybe just 1 turn (EDIT thinking again can even be zero tuns), and each step it gets more ?

 

[keemy]

Heh, I was just looking at this two or three days ago. Itai Bar-Natan was at MC10, although I don't recall seeing him with a cube at any point. Perhaps Raku or Devin actually attended the class in 09, we both went in the wrong year...

Didn't attend the class but got the handout from his colloquia (which is what the back side is about). I think raku or not-kevin may have gone as it was recommended that you take that before group theory and I think I saw them there.