WANTED: New Dedge Flip Algorithm!

[Christopher Mowla]

and an odd permutation always consists of an odd number of even-length cycles.

That.

 

[Stefan]

and an odd permutation always consists of an odd number of even-length cycles.

That.

Which is correct. What do you want?

 

[Christopher Mowla]

Look at post #73. This all leads back to that. (I didn't intend it to be a debate).

 

[qqwref]

cmowla: Look up some group theory please before you dig yourself any deeper into this hole. The definition of odd and even permutations are quite well-defined and any inconsistency you find will be in your own logic, not in the permutation concept itself.

reThinking: why are you calling it "OLDlucasparity™"?

 

[Christopher Mowla]

cmowla: Look up some group theory please before you dig yourself any deeper into this hole. The definition of odd and even permutations are quite well-defined and any inconsistency you find will be in your own logic, not in the permutation concept itself.

I know the difference between odd and even permutations. If there are an odd number of inversions, then it is an odd permutation and vice versa.

I even wrote a ti-83 plus program that solves the LL edges on a 4X4X4 (type in the sequence of the pieces and it returns the moves to solve the LL edges--assuming that the corners are solved already, the program finishes solving the cube).

 

[Stefan]

I know the difference between odd and even permutations. If there are an odd number of inversions, then it is an odd permutation and vice versa.

That's correct, so your problem is somewhere else. My money's currently on your understanding of "cycle".

 

[Lucas Garron]

reThinking: why are you calling it "OLDlucasparity™"?

Yeah, it's just lucasparity™, and the official definition is in SiGN™:

r U2 x r U2 r U2 r' U2 l U2 r' U2 r U2 r' U2 r'

 

[Christopher Mowla]

I know the difference between odd and even permutations. If there are an odd number of inversions, then it is an odd permutation and vice versa.

That's correct, so your problem is somewhere else. My money's currently on your understanding of "cycle".

If I am understanding the word "cycle" correctly now, does this mean that all 4 cycles are of odd permutations?

In other words, does "cycle" mean that the only way for the pieces to be swapped is all at once?

 

[Lucas Garron]

I know the difference between odd and even permutations. If there are an odd number of inversions, then it is an odd permutation and vice versa.

That's correct, so your problem is somewhere else. My money's currently on your understanding of "cycle".

If I am understanding the word "cycle" correctly now, does this mean that all 4 cycles are of odd permutations?

Close. They are odd permutations.

 

[Tim Reynolds]

I know the difference between odd and even permutations. If there are an odd number of inversions, then it is an odd permutation and vice versa.

That's correct, so your problem is somewhere else. My money's currently on your understanding of "cycle".

If I am understanding the word "cycle" correctly now, does this mean that all 4 cycles are of odd permutations?

In other words, does "cycle" mean that the only way for the pieces to be swapped is all at once?

Yes. A 4-cycle must be of the form (a b c d). It cannot be (a b)(c d), or (a)(b c d). Thus any 4-cycle is an odd permutation.

 

[Stefan]

If I am understanding the word "cycle" correctly now, does this mean that all 4 cycles are of odd permutations?

That's correct.

In other words, does "cycle" mean that the only way for the pieces to be swapped is all at once?

You can do it in several steps if you talk about the result. But mainly a cycle is a cycle.

The most common 4 cycle performed by speedcubers, r2 U2 r2 (Uu)2 r2 u2 is an even permutation cycle as well.

What you have here is not a 4-cyle but two 2-cycles.

 

[reThinking the Cube]

Given a 4x4x4 cube with all of the 24 edge pieces paired into their 12 respective dedges. Let's just ignore for now, all of the corners and center pieces.

#1) Does anyone know of some simple even#(2,4,6,8,.....24)-cycle algs to permute these edge pieces, that will also maintain the dedge pairing?

#2) Can Acube, or CubeX be used to generate possible algs for this type of problem?

reThinker

EDIT: Can also be any COMBINATION of cycles that permute these edges, as long as the total number of these even cycles is ODD.

 

[Stefan]

#1) Does anyone know of some simple even#(2,4,6,8,.....24)-cycle algs to permute these edge pieces, that will also maintain the dedge pairing?

Define "simple".

 

[reThinking the Cube]

#1) Does anyone know of some simple even#(2,4,6,8,.....24)-cycle algs to permute these edge pieces, that will also maintain the dedge pairing?

Define "simple".

I guess "simple" is <= 19q. And for the record - that doesn't include "U".


reThinker

 

[Stefan]

I guess "simple" is <= 19q.

Then the answer is yes, Lucas knows some.

 

[reThinking the Cube]

I guess "simple" is <= 19q.

Then the answer is yes, Lucas knows some.

YES! I would keep that game face on for as long as it takes to get him to share. You scared the hair off my back when I saw that!

reThinker

 

[Christopher Mowla]

Does anyone know what the briefest algorithm known to man is for the diagonal winged edge swap (pure form) in BQTM? (See sketch below).

I just need to know how many BQTM it is, not the algorithm itself or any other move measurements...

 

[reThinking the Cube]

Does anyone know what the briefest algorithm known to man is for the diagonal winged edge swap (pure form) in BQTM? (See sketch below).

I just need to know how many BQTM it is, not the algorithm itself or any other move measurements...

The answer is 2.

reThinker

 

[rachmaninovian]

Does anyone know what the briefest algorithm known to man is for the diagonal winged edge swap (pure form) in BQTM? (See sketch below).

I just need to know how many BQTM it is, not the algorithm itself or any other move measurements...

me would likey know the answer too.

 

[reThinking the Cube]

me would likey know the answer too.

I bet you would too. Checked out your sandwhich pages, http://rachmaninovian.webs.com/ This is becoming one of the best (clearest, and most complete) method descriptions for 4x4x4 (5x5x5). The page showing last dedge pair algs was especially interesting, and I saw that you tapped into many of the known good algs for doing those. I have a different method for solving 4x4x4 though, and would like to find better ways to do even-cycle edge perms. Would you likey know the answer for this previous post too?
http://www.speedsolving.com/forum/showpost.php?p=294116&postcount=90

reThinker