Compute all permutations of a given inequality in terms of coefficients matrix
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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:
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/199170/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/199171/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/199172/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/199173/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/199174/image.png)
So for 4 random variables
, we have (
)- dim (we consider only non-empty set) hyperplane in terms of coefficients as follows:
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/199175/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/199176/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/199177/image.png)
The inequality has 12 permutations (including itself) as follows:
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/199178/image.png)
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
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