# Descendants in heap ordered trees

or

a triumph of computer algebra

**Abstract.
A heap ordered tree with $n$ nodes (``size $n$'')
is a planted plane tree
together with a bijection from the nodes to the set $\{1,\dots,n\}$
which is monotonically increasing
when going from the root to the leaves.
We consider the number of descendants of the node $j$ in a (random)
heap ordered tree of size $n\ge j$.
Precise expressions are derived for
the probability distribution and all (factorial) moments.
**

** Related papers:**

Pathlength, etc.

Depth of nodes

helmut@gauss.cam.wits.ac.za,

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