TY - JOUR AU - Kazemi, Ramin AU - Delavar, Saeid PY - 2013 TI - The Moments of the Profile in Random Binary Digital Trees JO - Journal of Mathematics and Computer Science SP - 176-190 VL - 6 IS - 3 AB - 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 (\(t\geq 2\)) is asymptotically of the same order as the expected value (\(t=1\)). These results are derived by methods of analytic combinatorics. SN - ISSN 2008-949X UR - http://dx.doi.org/10.22436/jmcs.06.03.02 DO - 10.22436/jmcs.06.03.02 ID - Kazemi2013 ER -