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MathGroup Archive 1999

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Re: Enumerating Permutations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg20055] Re: [mg20006] Enumerating Permutations
  • From: BobHanlon at aol.com
  • Date: Wed, 29 Sep 1999 03:33:20 -0400
  • Sender: owner-wri-mathgroup at wolfram.com

Vic,

I believe what you are looking for is RankPermutation

Needs["DiscreteMath`Combinatorica`"]

perms = Permutations[Range[4]];

?RankPermutation

"RankPermutation[p] gives the rank of permutation p in lexicographic order."

RankPermutation[{3, 2, 1, 4}]

14

RankPermutation /@ perms

{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, \
21, 22, 23}


Bob Hanlon

In a message dated 9/25/1999 4:59:09 AM, fanberg at email.msn.com writes:

>I am looking for an algorithm for determining the Nth permutation (P) of
>a
>group T.  I don't really care the ordering of the permutations within T,
>as
>long as all the permutations of P are members of T exactly once.  (Each
>element of the permutation P is unique.)
>
>Actually, each of the permutations are only 7 digits long and I could list
>all 5040 permutations in a file about 35K, but I was hoping for something
>a
>little cleaner, in case I change to 8 or 9 digits long later.
>
>Does anyone know of such an algorithm?
>


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