1 citations · 1 across the 6 of their papers we have counts for
6 papers
Statistical Analysis of Hairpins and BasePairs in RNA Secondary Structures
AJ Bu, Manuel Kauers, Doron Zeilberger
We derive precise asymptotic expressions for the expectations, variances, covariance, and quite a few further mixed moments for the number of hairpins and the number of basepairs i…
A Short Proof that the number of -parking functions of length n
AJ Bu, Doron Zeilberger
We give a very short proof of the fact that the number of -parking functions of length equals . This was first proved in 2003 by Kung and Yan, via a very…
Explicit Expressions for the First 20 Moments of the Area Under Dyck and Motzkin Paths
AJ Bu, Shalosh B. Ekhad, Doron Zeilberger
Starting from AJ Bu's recent article that computed explicit expressions for the GENERATING functions of sums of powers of areas under Dyck and Motzkin paths, we deduce from them ex…
Explicit Generating Functions for the Sum of the Areas Under Dyck and Motzkin Paths (and for Their Powers)
AJ Bu
In this paper, we first describe how to find the generating function for the sum of the areas under generalized Dyck paths (with an arbitrary set of steps) using Motzkin paths as a…
Using Symbolic Computation to Explore Generalized Dyck Paths and Their Areas
AJ Bu, Doron Zeilberger
We show the power of Bruno Buchberger's seminal Groebner Basis algorithm, interfaced, seamlessly, with what we call symbolic dynamical programming, to automatically generate algebr…
Automated Counting of Restricted Motzkin Paths
AJ Bu
Motzkin paths are simple yet important combinatorial objects. In this paper, we consider families of Motzkin paths with restrictions on peak heights, valley heights, upward-run len…