="Mike Stay" <metaweta@gmail.com> Composition is associative, so I'd think you'd have a list rather than a tree. Can you expand a bit on what you're looking for?
I guess I'm seeking the "Official Name" for the tree data-structure analog that reflects the partitions vs. compositions distinction. Basically, A Tree is either a Leaf or an ordered sequence of sub-Trees. An X is either a Leaf or an unordered set of sub-X's. What do you call an X?
="Gareth McCaughan" <gareth.mccaughan@pobox.com> "Unordered tree"?
That's reasonable, but I don't want to coin a new term if there's already an existing one--which I suspect there may be, though for some reason I can't seem to recall what it is. As an "application", there's that nice categorical correspondence of 7-tuples of trees to trees, so what is the analog for X's--and so on.