Combinatorial enumeration of groups, graphs, and chemical compounds
Combinatorial enumeration of groups, graphs, and chemical compounds
On the profile of random trees
Random Structures & Algorithms
Convergence of branching processes to the local time of a Bessel process
proceedings of the eighth international conference on Random structures and algorithms
Laws of large numbers and tail inequalities for random tries and PATRICIA trees
Journal of Computational and Applied Mathematics - Special issue: Probabilistic methods in combinatorics and combinatorial optimization
On the covariance of the level sizes in random recursive trees
Random Structures & Algorithms
Nodes of large degree in random trees and forests
Random Structures & Algorithms
Profiles of random trees: Plane-oriented recursive trees
Random Structures & Algorithms
The distribution of patterns in random trees
Combinatorics, Probability and Computing
The distribution of nodes of given degree in random trees
Journal of Graph Theory
Analytic Combinatorics
SIAM Journal on Computing
The shape of unlabeled rooted random trees
European Journal of Combinatorics
The CRT is the scaling limit of unordered binary trees
Random Structures & Algorithms
The distribution of height and diameter in random non-plane binary trees
Random Structures & Algorithms
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We investigate the profile of random Polya trees of size n when only nodes of degree d are counted in each level. It is shown that, as in the case where all nodes contribute to the profile, the suitably normalized profile process converges weakly to a Brownian excursion local time. Moreover, we investigate the joint distribution of the number of nodes of degrees d"1 and d"2 on the same level of the tree.