Andre Engels wrote:
On Sun, Jun 14, 2009 at 6:49 PM, Paul
LaFollette<paul.lafolle...@gmail.com> wrote:
Now, suppose that I want to generate, say, the set of all ordered
trees with N nodes. I need to be able to represent the empty ordered
tree, i.e. the tree with with zero nodes. There are a lot of ways I
could do this. The problem is that I might tomorrow be looking
instead at rooted trees, or free trees, or Young tableaux and in each
case I will need to represent the empty rooted tree, or the empty free
tree, or the empty Young tableau.
In a very real sense, the empty Young tableau IS a Young tableau and
the empty ordered tree IS an ordered tree. But in an equally real
sense they are the same "ghost of a thing" looked at in different
universes of discourse.
But do you also want the empty Young tableau to BE an ordered tree? A
number? A diddlewoodaddy? It seems much more logical to me to define
your Young tableaus such that the definition includes the empty one as
well.
For strings there's the empty string with the same methods. It's not the
same as None.
For lists there's the empty list with the same methods. It's not the
same as None.
For dicts there's the empty dict with the same methods. It's not the
same as None.
For sets there's the empty set with the same methods. It's not the same
as None.
etc.
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