All row-combinations of a matrix in a new matrix with matlab

Question

I have got a question regarding all the combinations of matrix-rows in Matlab. I currently have a matrix with the following structure:

1 2 
1 3
1 4
2 3
2 4
3 4

Now I want to get all the possible combinations of these "pairs" without using a number twice in the same row:

1 2 3 4
1 3 2 4
1 4 2 3

And it must be possible to make it with n-"doublecolumns". Which means, when my pair-matrix goes for example until "5 6", i want to create the matrix with 3 of these doublecolumns:

1 2 3 4 5 6
1 2 3 5 4 6
1 2 3 6 4 5
1 3 2 4 5 6
1 3 2 5 4 6
....

I hope you understand what I mean :) Any ideas how to solve this?

Thanks and best regard Jonas

Answer 1

M = [1 2 
     1 3
     1 4
     2 3
     2 4
     3 4]; %// example data
n = floor(max(M(:))/2); %// size of tuples. Compute this way, or set manually

p = nchoosek(1:size(M,1), n).'; %'// generate all n-tuples of row indices
R = reshape(M(p,:).', n*size(M,2), []).'; %// generate result...
R = R(all(diff(sort(R.'))),:); %'//...removing combinations with repeated values