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Product of transpositions

  • To: mathgroup at
  • Subject: [mg17318] Product of transpositions
  • From: Carl Woll <carlw at>
  • Date: Fri, 30 Apr 1999 23:22:38 -0400
  • Organization: Physics Department, U of Washington
  • Sender: owner-wri-mathgroup at

Hi group,

I have a question/challenge.

Given a list of transpositions


where a,b,c... are all positive integers less than or equal to n,
produce the permutation, or cyclic decomposition of the product of the
transpositions. I don't care if you choose to multiply transpositions
left to right or right to left. As an example, the following list of


using right to left multiplication, will produce


or the cycle {a,b,c}. That is, using the usual notation, (ab)(bc)=(abc).
I hope this is clear.

If this functionality is built into a standard package, then tell me the
package. Otherwise, what is the fastest implementation that anyone can
come up with. I'm interested in repeatedly converting a random product
of 120 transpositions into the corresponding permutation.

Here is one idea.



Can anyone come up with a better idea?

Carl Woll
Dept of Physics
U of Washington

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