I want to construct all possible matrices with N elements. Example: if N=6, then I want a 1x6, 2x3 3x2 and 6x1 matrix. These matrices should all be unique. So if we consider a 2x3 matrix, the options would be: [1 2 3; 4 5 6], [1 2 4; 3 5 6], [1 2 5; 3 4 6], [1 2 6; 3 4 5], [1 3 4; 2 5 6], [1 3 5; 2 4 6], etc. For this matrix there will be 10 unique combinations. A similar expression for a 3x2 matrix can be obtained: [1 2; 3 4; 5 6], [1 2; 3 5; 4 6], [1 2; 3 6; 4 5], [1 3; 2 4; 5 6], etc. For this matrix there will be 15 unique combinations. The 1x6 and 6x1 matrices only contain 1 unique combination each. Note that the order of rows and the order within each row does not matter and each number can only be used once! So far, I did this manually for N=1:7. For a larger number of N, the number of combinations will explode. For N=12, there will be 32034 combinations possible...
I already did several attempts to obtain all possible matrices and searched for people who tackled similar problems . However, these options do not give the desired results. Can someone please help me? Thank you in advance!
