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Re: k-permutations enumeration

• To: mathgroup at smc.vnet.net
• Subject: [mg116446] Re: k-permutations enumeration
• From: Daniel Lichtblau <danl at wolfram.com>
• Date: Wed, 16 Feb 2011 04:32:26 -0500 (EST)

Michal Kvasnicka wrote:
> Once again... is there any enumeration (closed form) formula? The
> problem looks like simple combinatorics problem, but I can not find
> any relevant formula.
> 
> The above mentioned algorithms looks very good, but I am still looking
> for closed form formula.
> 
> Michal
> 

I do not believe there is a closed form in the sense you are seeking. 
The method/algorithm that looks like
Coefficient[Product[Sum[...]],...]
is, in some sense, a closed form. That is to say, there is a notation in 
the literature for exactly this computation. But like any special 
function, that does not imply the numeric computation will be trivial.

Daniel Lichtblau
Wolfram Research