Enumerating Alternating Trees

Enumerating Alternating Trees

In this paper we examine the enumeration of alternating trees. We give a bijective proof of the fact that the number of alternating unrooted trees with n vertices is given by 1 n2 n?1 P n k=1 ? n k k n?1 , a problem rst posed by Postnikov in 4]. We also prove, using formal arguments, that the number of alternating plane trees with n vertices is 2(n ? 1) n?1 .

Enumerating alternating tree families

We study two enumeration problems for up-down alternating trees, i.e., rooted labelled trees T , where the labels v1, v2, v3, . . . on every path starting at the root of T satisfy v1 < v2 > v3 < v4 > · · · . First we consider various tree families of interest in combinatorics (such as unordered, ordered, d-ary and Motzkin trees) and study the number Tn of different up-down alternating labelled ...

Enumerating Distinct Decision Trees

The search space for the feature selection problem in decision tree learning is the lattice of subsets of the available features. We provide an exact enumeration procedure of the subsets that lead to all and only the distinct decision trees. The procedure can be adopted to prune the search space of complete and heuristics search methods in wrapper models for feature selection. Based on this, we...

Enumerating k-Way Trees

This paper makes a contribution to the enumeration of trees. We prove a new result about k-way trees, point out some special cases, use it to give a new proof of Cayley’s enumeration formula for labelled trees, and observe that our techniques allow various types of k-way trees to be generated uniformly at random. We recall the definition: a k-way tree is either empty or it consists of a root no...

Enumerating the Prime Alternating Knots, Part Ii