Monotonic trees

[franktaw at netscape.net]

Actually, there is only one kind of direction: from the root to the 
leaf.
The difference is in what is being compared: out-degree or labels.  As
I noted, you can't have a monotonically increasing out-degree all the
way to the leaf (except for the one-node tree), since the leaves have
out-degree zero.

Thinning trees is not a bad alternative, though; in fact I almost
called them that.

Franklin T. Adams-Watters


-----Original Message-----
From: bowerc at usa.net

------ Original Message ------

> Define a rooted tree is monotonic if the out-degree (number of
> children)
> of every node is greater than or equal to the out-degree of any of its
> children.  How many monotonic trees are there with n nodes?
>
I've been thinking about the name "monotonic tree."

Monotonic normally means "increasing or decreasing."

"Increasing rooted tree" means a labeled RT that such that the numbers
on the labels increase on any path from root to leaf. Thus there are
two completely different types of direction being measured here.

Perhaps the name "thinning RTs" might be more appropriate or maybe

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