Abstract : q-binary search trees are obtained from words, equipped with a geometric distribution instead of permutations. The average and variance of the heighth computated, based on random words of length n, as well as a Gaussian limit law.
Michael Drmota, Helmut Prodinger. The height of q-Binary Search Trees. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2002, Vol. 5, pp.97-108. ⟨10.46298/dmtcs.304⟩. ⟨hal-00958975⟩