A Note on the Horton-Strahler Number for Random Binary Search Trees

Abstract We show that for a random binary search tree with n nodes and Horton-Strahler number Sn, lim n → ∞ P {S n ⩾ ( 1 log 3 + e) log n} = 0 , for all e >0. This result is confirmed by the experimental results of natural scientists and explains why the random binary search tree model is a poor choice for modeling the combinatorial structure of the human lung.

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