Message #584

From: Remigiusz Durka <thesamer@interia.pl>
Subject: Re: [MC4D] Re: Permutation formula updates
Date: Tue, 23 Sep 2008 10:49:33 +0200

Can I ask about formula as the input for program Mathematica (or Maxima, etc)… Or just see actual numbers for any hypercube we have?

all teh best,
RemiQ

—– Original Message —–
From: David Smith
To: 4D_Cubing@yahoogroups.com
Sent: Tuesday, September 23, 2008 2:50 AM
Subject: Re: [MC4D] Re: Permutation formula updates


Hi Thibaut,

    Thanks for your comments and suggestions!  I put a lot of thought into what<br>
    you recommended to me about the formulas, but I have decided to keep them the<br>
    same.  While I value your opinion, and almost did decide to modify the formulas,<br>
    I think that it is more concise and elegant to represent the answers with only one<br>
    formula.  While simplicity can be elegant, to me the formula is already so<br>
    (although this is of course my biased opinion as its discoverer).  I actually<br>
    never seperated the formulas into even/odd cases, and while many may not,<br>
    I like the use of the &quot;n mod 2&quot; terms and how I applied them.  If anyone on the<br>
    group is interested in a basic explanation as to the derivation of these formulas,<br>
    I would be glad to email them one.  I'm looking forward to using more advanced<br>
    reasoning for proving these formulas exact, and for trying my hand at the n&#94;5<br>
    and n&#94;d cases.  I'll let the group know when I get the super-supercube formula.

    All the Best,<br>
    David

    --- On Mon, 9/22/08, thibaut.kirchner &lt;thibaut.kirchner@yahoo.fr&gt; wrote&#58;

      From&#58; thibaut.kirchner &lt;thibaut.kirchner@yahoo.fr&gt;<br>
      Subject&#58; &#91;MC4D&#93; Re&#58; Permutation formula updates<br>
      To&#58; 4D&#95;Cubing@yahoogroups.com<br>
      Date&#58; Monday, September 22, 2008, 10&#58;53 AM


— In 4D_Cubing@yahoogrou ps.com, David Smith <djs314djs314@ …> wrote:
> I’ve updated my formula for the upper bound for the number of
> reachable positions of an n^4 Rubik’s cube (it contained
> some errors), and also finished a similar formula for the
> supercube. Until now, I’ve only been using combinatorial arguments
> and concepts of higher dimensions in my work.

      I'm amazed by the complexity of the formula. I suggest you to split it<br>
      into two formulas, one for the odd-sized hypercubes, and on for the<br>
      even-sized hypercubes. I'm sure the two formulas would be easier to<br>
      read than this one, and I'm not sure it's interesting to group the two<br>
      formulas into a single one.<br>
      Also, if you put the factors associated with a single type of piece by<br>
      row, it could help the reader (and group somewhere the constraints<br>
      which link several type of piece).

      Thibaut.