Enumerative combinatorics
On the complexity of algorithms on recursive trees
Theoretical Computer Science
On the total heights of random rooted binary trees
Journal of Combinatorial Theory Series B
On the distribution of binary search trees under the random permutation model
Random Structures & Algorithms
Poisson approximations for functionals of random trees
Proceedings of the seventh international conference on Random structures and algorithms
Limit distribution for the maximum degree of a random recursive tree
Journal of Computational and Applied Mathematics - Special issue: Probabilistic methods in combinatorics and combinatorial optimization
Cost distribution of the Chang-Roberts leader election algorithm and related problems
Theoretical Computer Science
The structure and distances in Yule recursive trees
Random Structures & Algorithms
Depth Properties of scaled attachment random recursive trees
Random Structures & Algorithms
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Total path length, or search cost, for a rooted tree is defined as the sum of all root-to-node distances. Let Tn be the total path length for a random recursive tree of order n. Mahmoud [10] showed that Wn := (Tn − E[Tn])/n converges almost surely and in L2 to a nondegenerate limiting random variable W. Here we give recurrence relations for the moments of Wn and of W and show that Wn converges to W in Lp for each 0 p W is not normal. We also show that the distribution of W is characterized among all distributions having zero mean and finite variance by the distributional identity***** Insert equation here *****where ℰ(x) := − x ln x − (1 minus; x) ln(1 − x) is the binary entropy function, U is a uniform (0, 1) random variable, W* and W have the same distribution, and U, W and W* are mutually independent. Finally, we derive an approximation for the distribution of W using a Pearson curve density estimator.