Valency enumeration of rooted plane trees

Enumeration of Weighted Plane Trees

In weighted trees, all edges are endowed with positive integral weight. We enumerate weighted bicolored plane trees according to their weight and number of edges. 1 Preliminaries This note is not intended for a journal publication: it does not contain difficult results, and the proofs use only standard and well-known techniques. Furthermore, some of the results are already known. However, they ...

4-PLACEMENT OF ROOTED TREES

A tree T of order n is called k-placement if there are k edge-disjoint copies of T into K_{n}. In this paper we prove some results about 4-placement of rooted trees.

Twelve Countings with Rooted Plane Trees

The average number of (1) antichains, (2) maximal antichains, (3) chains, (4) infima closed sets, (5) connected sets, (6) independent sets, (7) maximal independent sets, (8) brooms, (9) matchings, (10) maximal matchings, (11) linear extensions, and (12) drawings in (of) a rooted plane tree on n vertices is investigated. Using generating functions we determine the asymptotics and give some expli...

The Enumeration of Rooted Trees by Total Height

The height (as in [3] and [4]) of a point in a rooted tree is the length of the path (that is, the number of lines in the path) from it to the root; the total height of a rooted tree is the sum of the heights of its points. The latter arises naturally in studies of random neural networks made by one of us (N.J.A.S.), where the enumeration of greatest interest is that of trees with all points di...

On the enumeration of rooted trees with fixed size of maximal decreasing trees