Message #3360

From: Melinda Green <melinda@superliminal.com>
Subject: Re: [MC4D] Re: About the number of permutations of MC4D calculating
Date: Sat, 21 May 2016 22:31:24 -0700

OK, I’ve made the changes at the bottom of the permutations page
<http://superliminal.com/cube/permutations.html>. If anyone is curious
and able to verify it, I’d appreciate it.
Thanks Joel!
-Melinda

On 5/8/2016 5:50 AM, joelkarlsson97@gmail.com [4D_Cubing] wrote:
>
> I believe that the factors should be arranged like this:
> B: 6^31 * 12^15*4 * 16!
> S: 6^32/2 * 12^16/3 * 16!/2
>
> Like Pham pointed out, the middle factors (regarding orientation of
> corner pieces) are matching.
>
> The first factor is probably, as Pham said, about the orientation of
> central edge pieces (since it’s a group of 32 pieces). David V has
> already proven that Smith is correct here since the orientation of the
> last of those pieces is limited by 1/2 (see:
> https://groups.yahoo.com/neo/groups/4D_Cubing/conversations/topics/2136)
>
>
> The third is indeed about corner permutation. It seems like Balandraud
> missed to account for the parity of the permuta tions of corner pieces
> and that Smith is correct in this regard as well.
>
> To conclude, Balandraud seems to have missed that the last central
> edge piece (3C piece) can have three different orientations and that
> the parity of permutations of corner pieces always are even. Thus, I
> suggest that Melinda changes the count at Superliminal to the value
> provided by Smith Wolfram|Alpha: Computational Knowledge Engine
> <http://www.wolframalpha.com/input/?i=%2816%21%2F2%29+*+%2824%21*32%21%2F2%29+*+64%21%2F2+*+%2896%21%2F24%5E24%29%5E2+*+64%21%2F%288%21%29%5E8+*+96%21%2F%2812%21%29%5E8+*+48%21%2F%286%21%29%5E8+*+12%5E16%2F3+*+6%5E32%2F2+*+3%5E64%2F3+*+2%5E24%2F2+*+%282%5E96%2F2%29%5E2>)