Message #489

From: Roice Nelson <roice3@gmail.com>
Subject: Re: [MC4D] Introduction to the 4D_Cubing Group
Date: Sun, 04 May 2008 10:30:06 -0500

Excellent, this sounds like a great approach. If you are interested in
writing it up, I’m sure some would enjoy reading about your general
algorithm to cycle 3 pieces of any type, but not worries too if you don’t
feel like doing it (if you’d rather just focus on the problem :))

I’ll let Eric and/or others comment on the possible 5^4 permutation
calculation issues for now because I’ll still need to hunker down and do
some study myself before I’m in a position to contribute there.

All the best,

Roice

P.S. As a teaser, I’m going to present a new permutation calculation problem
soon (hopefully this evening) that I hope you guys will be able to help me
figure out!

On Sat, May 3, 2008 at 10:02 PM, David Smith <djs314djs314@yahoo.com> wrote:

> Hi Roice,
>
> Once again, thank you for all of your help! I really appreciate
> the time you take to reply with your excellent advice.
>
> Right after I read your post, I had an idea for achieving what
> I want to do without writing a program at all! My idea basically
> consists of discovering general algorithms (using MagicCube4D) that
> can show that any possible permutation within the constraints I
> will discover is possible, for any sized cube. I have taken some
> algorithms from Keane and Kamack’s paper as given, which will help
> me. If I decide to do 5-dimensional cubes after this, I will not
> have this luxury! The MagicCube4D program is essential for
> discovering the required algorithms, so I do not think I will
> discover a general formula for any-sized any-dimensional cubes
> without an advanced group theory approach (although I may discover
> the upper bound without proving equality).
>
> Right now, I am working out the final details of a general algorithm
> that can perform a 3-cycle of any three hypercubies in the same
> family on any sized cube. This only produces any even permutation,
> but I will also show that for an arbitrarily-sized cube, certain
> permutation parity restrictions exist, and will also show that all
> of the other parities can be generated. Then, my 3-cycle algorithm
> will show that for each possible parity condition, I can generate
> any possible permutations for that parity, and this means that all
> possible permutations can be reached. If you want the details of
> this algorithm, I can email them to you (or post it on this group,
> whichever you feel is most appropriate) and send you macro files
> showing some specific examples of the general algorithm. I still
> have to do something similar for orientations, although Keane
> and Kamack’s paper helps me out with the corner and central edge
> algorithms they discovered.
>
> I have also discovered what I believe to be two mistakes in the
> calculation of the 5x5x5x5 cube’s permutations on the MagicCube4D
> website written by Eric Balandraud. They appear to be fairly
> obvious mistakes (once you understand the logic of the paper), and
> I would not say this if I were not at least 95% certain of it, but
> anyone may feel free to correct me if I am wrong. I think that
> the term ((3!)^31) should be (((3!)^31)*3) and that the term
> (16!) should be ((16!)/2), making the answer given correct if we
> multiply it by (3/2). The author of the paper has clearly shown
> himself to be very proficent in this area, so I believe these
> errors are typos or an oversight, but once again, anyone please
> let me know if I am wrong.
>
> Once again, Roice, thank you for your advice and support. I look
> forward to hearing from you!
>
> Best Regards,
>
> David
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