MATLAB Central Newsreader - I want to know the number of permutations.

I want to know the number of permutations.

Husam Aldahiyat — Mon, 29 Jun 2009 15:16:02 -0400

Hello,
Just like we do with nchoosek, I want a way to obtain the number of rows of the output of perms, without obtaining what they are.

Please help!

Specifically, I want the following:

length(unique(perms([ones(1,20),zeros(1,20)])))

or

length(perms([ones(1,20),zeros(1,20)]))/400

(I think they give the same result)

end

Re: I want to know the number of permutations.

Bruno Luong — Mon, 29 Jun 2009 15:36:01 -0400

"Husam Aldahiyat" <numandina@gmail.com> wrote in message <h2alri$2o3$1@fred.mathworks.com>...
> Hello,
> Just like we do with nchoosek, I want a way to obtain the number of rows of the output of perms, without obtaining what they are.
>
> Please help!
>
> Specifically, I want the following:
>
> length(unique(perms([ones(1,20),zeros(1,20)])))

% I guess you miss 'rows'
m = 2;
n = 6;
p=unique(perms([ones(1,m),zeros(1,n)]),'rows');

size(p,1) == nchoosek(m+n,n)

% Bruno

Re: I want to know the number of permutations.

Alan B — Mon, 29 Jun 2009 15:44:02 -0400

"Husam Aldahiyat" <numandina@gmail.com> wrote in message <h2alri$2o3$1@fred.mathworks.com>...
> Hello,
> Just like we do with nchoosek, I want a way to obtain the number of rows of the output of perms, without obtaining what they are.
>
> Please help!
>
> Specifically, I want the following:
>
> length(unique(perms([ones(1,20),zeros(1,20)])))
>
> or
>
> length(perms([ones(1,20),zeros(1,20)]))/400
>
> (I think they give the same result)
>
> end

If you're just interested in examples similar to the one you give, look at this: http://www.research.att.com/~njas/sequences/index.html?q=2+6+20+70+252&language=english&go=Search .

Re: I want to know the number of permutations.

Husam Aldahiyat — Mon, 29 Jun 2009 15:45:03 -0400

"Bruno Luong" <b.luong@fogale.findmycountry> wrote in message <h2an11$k7n$1@fred.mathworks.com>...
> "Husam Aldahiyat" <numandina@gmail.com> wrote in message <h2alri$2o3$1@fred.mathworks.com>...
> > Hello,
> > Just like we do with nchoosek, I want a way to obtain the number of rows of the output of perms, without obtaining what they are.
> >
> > Please help!
> >
> > Specifically, I want the following:
> >
> > length(unique(perms([ones(1,20),zeros(1,20)])))
>
> % I guess you miss 'rows'
> m = 2;
> n = 6;
> p=unique(perms([ones(1,m),zeros(1,n)]),'rows');
>
> size(p,1) == nchoosek(m+n,n)
>
> % Bruno

Actually I used rows in my code I just forgot to put it in the message.

About your code, I don't understand the final line. I have a headache please bear with me! And I want m and n to be 20 and 20. That's why I'm looking for a getaround, because the matrix for perms would be very big to do it normally :(

Re: I want to know the number of permutations.

Husam Aldahiyat — Mon, 29 Jun 2009 15:52:01 -0400

Wow it was nchoosek(40,20) all along!!! Why didn't I see that!

Thanks for the help, and the link is very helpful, thanks a lot Alan B.

Re: I want to know the number of permutations.

Husam Aldahiyat — Mon, 29 Jun 2009 16:02:01 -0400

"Husam Aldahiyat" <numandina@gmail.com> wrote in message <h2anv1$m0g$1@fred.mathworks.com>...
> Wow it was nchoosek(40,20) all along!!! Why didn't I see that!
>
> Thanks for the help, and the link is very helpful, thanks a lot Alan B.

I think Alan B's link givers the fastest method for this case.

factorial(40)/(factorial(20))^2

By the way this is the answer to the following question:

In a 20 by 20 square grid, how many ways can one travel from one corner to the opposite without backtracking.

Re: I want to know the number of permutations.

Bruno Luong — Mon, 29 Jun 2009 16:11:02 -0400

"Husam Aldahiyat" <numandina@gmail.com> wrote in message <h2aohp$1mm$1@fred.mathworks.com>...

>
> In a 20 by 20 square grid, how many ways can one travel from one corner to the opposite without backtracking.

The general case is showed here, if you haven't pay attention
http://www.mathworks.com/matlabcentral/newsreader/view_thread/253745#658145

Bruno