Counting

*To*: mathgroup at smc.vnet.net*Subject*: [mg114850] Counting*From*: Yaroslav Bulatov <yaroslavvb at gmail.com>*Date*: Mon, 20 Dec 2010 00:40:07 -0500 (EST)

I'd like to count the number of permutations of {2, 2, 2, 2, 2, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0} that are not equivalent under the symmetry of DihedralGroup[16]. In other words, count the ways of assigning those integers to vertices of a 4 dimensional cube. This takes about a minute in another systme using "OrbitsDomain" command. My Mathematica approach is below, however it doesn't finish within 10 minutes, any advice how to make it tractable? nonequivalentPermutations[lst_, group_] := ( removeEquivalent[{}] := {}; removeEquivalent[list_] := ( Sow[First[list]]; equivalents = Permute[First[list], #] & /@ GroupElements[group]; DeleteCases[list, Alternatives @@ equivalents] ); reaped = Reap@FixedPoint[removeEquivalent, Permutations@lst]; reaped[[2, 1]] // Length ); nonequivalentPermutations[{2, 2, 2, 2, 2, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0}, DihedralGroup[16]]

**Follow-Ups**:**Re: Counting***From:*Leonid Shifrin <lshifr@gmail.com>

**Re: Counting***From:*Leonid Shifrin <lshifr@gmail.com>

**Re: Counting***From:*Leonid Shifrin <lshifr@gmail.com>