[Date Index]
[Thread Index]
[Author Index]
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!
Prev by Date:
**Re: help with DictionaryLookup[] and a type of regular expression**
Next by Date:
**Re: Variables in Iterator limits?**
Previous by thread:
**Re: and a type of regular expression**
Next by thread:
**Re: help with DictionaryLookup[] and a type of regular**
| |