3 papers
math.CO2024
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…
math.CO2024
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…
math.CO2020
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…