Re: All permutations of a sequence

*To*: mathgroup at smc.vnet.net*Subject*: [mg76216] Re: All permutations of a sequence*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>*Date*: Fri, 18 May 2007 06:02:59 -0400 (EDT)*Organization*: The Open University, Milton Keynes, UK*References*: <f2h8t7$v4$1@smc.vnet.net>

Virgil Stokes wrote: > I would like to get all unique permutations of a sequence (e.g. > {1,2,3,4,5,6,7,8,9,10,11,12,13}) with the constraint that all sequences > that have an opposite ordering are not included (e.g. {13, 12, > 11,10,9,8,6,5,4,3,2,1}) would not be included. > > Are there some Mathematica commands that can be used to efficiently > generate these permutations? > > --V. Stokes Hi Virgil, Assuming that I have correctly understood your request, the following code should do what you are looking for. (Note that the function is recursive. You may have to adjust the system parameter $RecursionLimit to a higher value than the default of 256. Also, if the list is large, this approach can become quickly inefficient). In[1]:= mySearch[l_List] := Module[{e = First[l], r = Rest[l]}, Sow[e]; mySearch[DeleteCases[r, x_ /; x == Reverse[e]]]; ] /; Length[l] > 1 lst = {1, 2, 3, 4, 2}; << "DiscreteMath`Combinatorica`" p = DistinctPermutations[lst]; q = Reap[mySearch[p]][[2,1]]; {Length[p], Length[q], Sort[p] == Sort[Join[q, Reverse /@ q]]} Out[6]= {60, 30, True} Regards, Jean-Marc