Monotonic trees

[Brendan McKay]

Top-heavy trees.


* franktaw at netscape.net <franktaw at netscape.net> [061021 02:01]:
> 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 ------
> Received: Wed, 18 Oct 2006 10:39:46 AM PDT
> 
> >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
> someone on the list can think of a better name.
> 
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