Re: Help ! complex permutations

*To*: mathgroup at smc.vnet.net*Subject*: [mg7030] Re: Help ! complex permutations*From*: uyurtsever at dynatec.com (Ulvi Yurtsever)*Date*: Fri, 2 May 1997 21:30:55 -0400 (EDT)*Organization*: AT&T WorldNet Services*Sender*: owner-wri-mathgroup at wolfram.com

On 29 Apr 1997 21:40:11 -0400, Robert_P at pro-bel.co.uk (Robert Perkins) wrote: >I need to derive an algorithm, formula, which gives all the >possiblities, combinations, for any 'n' out of 'm' with the proviso >that any member of 'm' can be used multiple times and the selection >sequence is significant. > >Taking a trivial example if the input list 'm' is > > {a,b} > >the output list 'n' for any 2 gives > > {a,a},{a,b},{b,a},{b,b} > >For an output sequence of 3 from the same input list would give > > {a,a,a},{a,a,b},{a,b,b},{b,a,b},{b,b,a},{b,b,b} You forgot {a,b,a} and {b,a,a}, I think... > >Life gets interesting for larger input sequences and ever larger >output selections. How about the input list containing 10 members and >the output list containing 20 members with the above rules applying? > >Can anyone point me in the right direction? A reference, clue or even >an algorithm would be very welcome ;) > >TIA > >Robert_p Why isn't this set of all possible combinations simply the cartesian product mXmXmX...Xm, where the product has as many terms as the number of elements n you want in the output? The total number of all possible combinations is then |m|^n, and Mathematica has a list-product function called Outer which will compute the cartesian product set for you. hope this is helpful