I am working with a function of type
that obeys the following symmetries:
i.e. is symmetric in entries 1-2,3-4 and 5-6 and also is symmetric if I switch any couple of entries with a different one. I want to compute a list with all the possible distinct values of the function, giving different entries. To do this, I want to compute a list of lists containing all the possible distinct orderings of my entries (given the symmetries of my function). From a simple combinatorics argument, I expect
different orderings of my entries. To be more specific, the different orderings I need are
How can I compute those distinct orderings in Mathematica? Can I exploit some specific features of Permutation command?