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