I have a group of 6 objects, that I want to put into 2 groups of 3. I know there are 20 combinations, but simultaneously there are only 10 combinations as the others are redundant. How do I programatically (probably using functions from igraph??) develop a general solution? Ultimately, I'll want to take a group of 40 objects and put them in groups of 10. The table below illustrates all the unique simultaneous sets for 2 groups of 6 objects.
a b c | d e f | 001 a b d | c e f | 002 a b e | c d f | 003 a b f | c d e | 004 a c d | b e f | 005 a c e | b d f | 006 a c f | b d e | 007 a d e | b c f | 008 a d f | b c e | 009 a e f | b c d | 010