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Re: Number of ways of permutations to form a certain pattern of

  • To: mathgroup at smc.vnet.net
  • Subject: [mg109654] Re: Number of ways of permutations to form a certain pattern of
  • From: newlearner <poincare100 at gmail.com>
  • Date: Mon, 10 May 2010 06:39:18 -0400 (EDT)
  • References: <hs3gl2$rvo$1@smc.vnet.net>

On May 8, 7:07 pm, newlearner <poincare... at gmail.com> wrote:
> Dear all,
>
> How to compute in Mathematica the number of ways of permutations of n-
> objects to form a certain pattern of cycles?
> I mean, for example, let n = 3. then there are 6 ways of permutations
> of three objects
>
> 123, 231, 312, 132, 213, 321
>
> Among them, we have the three 1-cycle pattern, 123
> two 3-cycle pattern, 231, 312
> one 1-cycle and one 2-cycle pattern, 132, 213, 321
>
> How to calculate this kind of mathematical problem with Mathematica?
> Could you also show me how to calculate the number of ways without
> using of Mathematica?
>
> Thanks so much!

Thank you guys.
I finally used the function "ToCycles"
to obtain all permutations in the form of cycles.
Then I used the "Select" function to filter the permutations that I
want.
By the way, I found in mathworld that the ToCycles function was
a challenge in Mathematica programming.

By the way, I wonder that if Mathematica can do tensor algebra?
For example, the Levi Civita symbol is implemented in Mathematica as
"Signature" function.
However, the output of the "Signature" function is a number,
this seems to obscure the possible tensor algebra involving the Levi
Civita symbol?

Any ideas or solutions?
Many thanks!


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