Re: General--Simple Permutations

*To*: mathgroup at smc.vnet.net*Subject*: [mg70382] Re: [mg70333] General--Simple Permutations*From*: "Adriano Pascoletti" <pascolet at dimi.uniud.it>*Date*: Sun, 15 Oct 2006 00:18:44 -0400 (EDT)

andrew.and.liz at gmail.com wrote .. > I would like to write a function that can look at a long list of permutations > (an output from other calculations) and list, in cycle form, only the permutations > that consist of 2 cycles or 3 cycles and leave the rest of the places alone. > I am analyzing a permutation puzzle and am looking for short sequences > of moves that switch a few places and leave the rest of the pieces in place. > Any help would be appreciated! > Andrew, look at the function ToCycles in the Combinatorica package In[1]:= << "DiscreteMath`Combinatorica`" In[2]:=?ToCycles ToCycles[p] gives the cycle structure of permutation p as a list of cyclic \ permutations. then evaluate Cases[<long listof perms>,p_/;2≤Length[ToCycles[p]]≤3] For instance In[4]:= Cases[Permutations[3], p_ /; 2 <= Length[ToCycles[p]] <= 3] Out[4]= {{1, 2, 3}, {1, 3, 2}, {2, 1, 3}, {3, 2, 1}} and In[5]:= Cases[Permutations[4], p_ /; 2 <= Length[ToCycles[p]] <= 3] Out[5]= {{1,2,4,3},{1,3,2,4},{1,3,4,2},{1,4,2,3},{1,4,3,2},{2,1,3,4},{ 2,1,4,3},{2,3,1,4},{2,4,3,1},{3,1,2,4},{3,2,1,4},{3,2,4,1},{ 3,4,1,2},{4,1,3,2},{4,2,1,3},{4,2,3,1},{4,3,2,1}} Adriano Pascoletti