Surely you're not serious when you say "computer scientists don't know that things come in "unordered"? Are you saying that it was invading mathematicians that were responsible for such data types as dictionaries and sets in various programming languages from PostScript to Python? And do you not count as computer scientists those who work on graph algorithms? --ms On 7/12/2012 10:49 AM, Michael Kleber wrote:
To mathematicians, X = Tree. The thing that cares what order the children are in is called a "planar tree" instead.
Computer scientists don't know that things come in "unordered", so they dropped the word "planar" and just call the ordered things trees.
--Michael
On Thu, Jul 12, 2012 at 10:16 AM, Marc LeBrun <mlb@well.com> wrote:
="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.
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