49 research outputs found
On the number of vertices of each rank in phylogenetic trees and their generalizations
We find surprisingly simple formulas for the limiting probability that the
rank of a randomly selected vertex in a randomly selected phylogenetic tree or
generalized phylogenetic tree is a given integer.Comment: 7 pages, 1 figur
Long and short paths in uniform random recursive dags
In a uniform random recursive k-dag, there is a root, 0, and each node in
turn, from 1 to n, chooses k uniform random parents from among the nodes of
smaller index. If S_n is the shortest path distance from node n to the root,
then we determine the constant \sigma such that S_n/log(n) tends to \sigma in
probability as n tends to infinity. We also show that max_{1 \le i \le n}
S_i/log(n) tends to \sigma in probability.Comment: 16 page
The MacLisp Reference
[16] B. Pittel, Note on the heights of random recursive trees and random m-ary search trees, Rand. Struct. Alg. 5 337-347 (1994)