The moments of the profile in random binary digital trees

The purpose of this paper is to provide a precise analysis of the t
-th moment of the profile in random binary digital trees. We assume that the n input strings are independent and follow a (binary) Bernoulli model. In tries, the main difference with the previous analysis is that we have to deal with an inhomogeneous part in the proper functional equation satisfied by the t
-th moment and in digital search trees with an inhomogeneous part in a proper functional-differential equation. We show that
t-th moment of the profile (
t > =2 ) is asymptotically of the same order as the expected value (
t=1). These results are derived by methods of analytic combinatorics.