Compute all permutations of a given inequality in terms of coefficients matrix

Hello friends,

I have inequality say , where denotes the mutual information between and . The canonical form of the above inequality can be written in terms of entropies as follows:

.

So for 4 random variables , we have ()- dim (we consider only non-empty set) hyperplane in terms of coefficients as follows:

The inequality has 12 permutations (including itself) as follows:

Manually I have calculated all the above permutations.

For a given inequality, I want to compute all permutations by a program. Please help me.

Thanks in advance.

#MSA