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How to Permute Column of a Matrix

Okkes Dulgerci
Posted 10 years ago

Hi All, I have 5x4 matrix. I want to permute only element of columns such that each rows contains the same letter exactly once.

Here is my matrix

enter image description here

One possible matrix is m1 in the picture. I want to generate all matrix similar to m1. Exchange of column is not allowed.

Here is the code:

list = {a, b, c, d, e};

m = Table[Subscript[#, i], {i, 4}] & /@ list; MatrixForm@m

Any suggestions?

Thanks in advance..
POSTED BY: Okkes Dulgerci
4 Replies
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Without access to Mathematica (desktop) I would suggest you look into Latin Rectangles, Circulants Matrix, or Toeplitz Matrices.

http://mathworld.wolfram.com/CirculantMatrix.html

and http://mathworld.wolfram.com/ToeplitzMatrix.html
POSTED BY: Hans Michel
Bill Simpson
Bill Simpson
Posted 10 years ago

Think how many permutations of the first column there can be, now many of the second, ... think how many matricies you will have when you "want to generate all matrix." Is that perhaps a problem?

Think why first doing Transpose, then doing some other things and finally doing another Transpose might be interesting.

Think what that "then doing some other things" might be.

Is this possibly related to a homework problem?
POSTED BY: Bill Simpson
Okkes Dulgerci
Okkes Dulgerci
Posted 10 years ago

Hi Bill, Thank you for your reply. No, it is not related to HW. I know there are 

5! 4! 3! 2! 
=34560

possibilities.. I can't take the transpose, because it will change the my problem..

Thanks,
POSTED BY: Okkes Dulgerci
Bill Simpson
Bill Simpson
Posted 10 years ago
POSTED BY: Bill Simpson
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