A q-analogue of the path length of binary search trees
A reformulation of the path length of binary search trees is given in terms of permutations, allowing us to extend the definition to the instance of words, where the letters are obtained by independent geometric random variables (with parameter q). In this way, expressions for expectation and variance are obtained which in the limit for q --> 1 are the classical expressions.
q-analogues path length binary search tree permutations geometric distribution harmonic numbers