Monotonic trees

[Christian G. Bower]

------ Original Message ------
From: franktaw at netscape.net
To: seqfan at ext.jussieu.fr
Subject: Monotonic trees

> 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.

Christian

P.S.

We can also count increasing MRTs as

1 1 2 5 19 87 484 3110 22869 188938 1735684 17544342 193537909
2313316683 29780777636 410783319119 6043874244604 94478706232996