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Re; Tally[ ] and Union[ ]
I immediately suspected Combinatorica`IsomorphicQ. I was able to convince myself, however, that IsomorphicQ is symmetric and transitive over the set of 21 graphs produced by diagrams. Do we ask any more of a test for equivalence? If not, then suspicion reverts to Tally, which is yielding too many results. I've no answer. > "A sorted Tally is equivalent to a list of counts for the Union:" > > This is what I indeed expect of Tally and Union, in particular then > it holds for any list: Length[Tally[list]] is equal to Length > [Union[list]].