Message #3407

Subject: Calculate number of permutation of restricted cube
Date: Wed, 29 Jun 2016 06:59:49 -0700

I want to calculate number of permutation of half-turn-only 2^4 cube.

First, I split the cubies into two groups, called "even" and "odd" ones. Fix one piece in odd group. The permutation in each group is even. Thus an upper bound is 8!/2 * 7!/2.

Intuitively I think single 3-cycle in each group is impossible, so there is much less permutation. But I can’t think how to prove it.

Using computer brute force, there are 1344 (surprisingly small) permutations, if the program has no bug.