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!