Asymptotic expectation of protected node profile in random digital search trees

Protected nodes are neither leaves nor parents of any leaves in a rooted tree. We study here protected node profile, namely, the number of protected nodes with the same distance from the root in digital search trees, some fundamental data structures to store 0 - 1 strings. When each string is a sequence of independent and identically distributed Bernoulli(p) random variables with 0 < p < ( p≠12 p \ne {1 \over 2} ), Drmota and Szpankowski (2011) investigated the expectation of internal profile by the analytic methods. Here, we generalize the main parts of their approach in order to obtain the asymptotic expectations of protected node profile and non-protected node profile in digital search trees.