منابع مشابه
Descendants in Increasing Trees
Simple families of increasing trees can be constructed from simply generated tree families, if one considers for every tree of size n all its increasing labellings, i. e. labellings of the nodes by distinct integers of the set {1, . . . , n} in such a way that each sequence of labels along any branch starting at the root is increasing. Three such tree families are of particular interest: recurs...
متن کاملA Combinatorial Approach for Analyzing the Number of Descendants in Increasing Trees and Related Parameters
This work is devoted to a study of the number of descendants of node j in random increasing trees, previously treated in [4, 6, 8, 13], and also to a study of a more general quantity called generalized descendants, which arises in a certain growth process. Our study is based on a combinatorial approach by establishing a bijection with certain lattice paths. For the parameters considered we deri...
متن کاملDescendants and ascendants in binary trees
There are three classical algorithms to visit all the nodes of a binary tree – preorder, inorder and postorder traversal. From this one gets a natural labelling of the n internal nodes of a binary tree by the numbers 1; 2; : : : ; n, indicating the sequence in which the nodes are visited. For given n (size of the tree) and j (a number between 1 and n), we consider the statistics number of ascen...
متن کاملThe Number of Descendants in Simply Generated Random Trees
The aim of this note is to generalize some recent results for binary trees by Panholzer and Prodinger [15] to a larger class of rooted trees. The number of descendants of a node j is the number of nodes in the subtree rooted at j, and the number of ascendants is the number of nodes between j and the root. Recently, Panholzer and Prodinger [15] studied the behavior of these parameters in binary ...
متن کاملIncreasing paths in regular trees
We consider a regular n-ary tree of height h, for which every vertex except the root is labelled with an independent and identically distributed continuous random variable. Taking motivation from a question in evolutionary biology, we consider the number of simple paths from the root to a leaf along vertices with increasing labels. We show that if α = n/h is fixed and α > 1/e, the probability t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2006
ISSN: 1077-8926
DOI: 10.37236/1034