An introduction to the analysis of algorithms
An introduction to the analysis of algorithms
Journal of Combinatorial Theory Series A
Deformations of Coxeter hyperplane arrangements
Journal of Combinatorial Theory Series A
Journal of Combinatorial Theory Series A
Concrete Mathematics: A Foundation for Computer Science
Concrete Mathematics: A Foundation for Computer Science
On the degree distribution of the nodes in increasing trees
Journal of Combinatorial Theory Series A
Analytic Combinatorics
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We study two enumeration problems for up-down alternating trees, i.e., rooted labelled trees T, where the labels v"1,v"2,v"3,... on every path starting at the root of T satisfy v"1v"3.... First we consider various tree families of interest in combinatorics (such as unordered, ordered, d-ary and Motzkin trees) and study the number T"n of different up-down alternating labelled trees of size n. We obtain for all tree families considered an implicit characterization of the exponential generating function T(z) leading to asymptotic results of the coefficients T"n for various tree families. Second we consider the particular family of up-down alternating labelled ordered trees and study the influence of such an alternating labelling to the average shape of the trees by analyzing the parameters label of the root node, degree of the root node and depth of a random node in a random tree of size n. This leads to exact enumeration results and limiting distribution results.