91 citations · 520 across the 230 of their papers we have counts for
13 papers · 1 filter
The C-finite Ansatz Meets the Holonomic Ansatz
Shalosh B. Ekhad, Doron Zeilberger
We show how the continuous Almkvist-Zeilberger algorithm can be used to efficiently discover and prove differential equations satisfied by generating functions of sequences defined…
Computerizing the Andrews-Fraenkel-Sellers Proofs on the Number of m-ary partitions mod m (and doing MUCH more!)
Shalosh B. Ekhad, Doron Zeilberger
In this short article, two recent beautiful proofs of George Andrews, Aviezri Fraenkel, and James Sellers, about the mod m characterization of the number of m-ary partitions are si…
Searching for Disjoint Covering Systems with Precisely One Repeated Modulus
Shalosh B. Ekhad, Aviezri S. Fraenkel, Doron Zeilberger
A set of arithmetical sequences with $$…
Surprising Relations Between Sums-Of-Squares of Characters of the Symmetric Group Over Two-Rowed Shapes and Over Hook Shapes
Amitai Regev, Doron Zeilberger
In a recent article (arXiv:1507.03499) (joint with Alon Regev) we studied sums of squares of characters Chi(L,M) of the Symmetric Group over shapes L that are two-rowed, and shapes…
Automated Discovery and Proof of Congruence Theorems for Partial Sums of Combinatorial Sequences
William Y. C. Chen, Qing-Hu Hou, Doron Zeilberger
Many combinatorial sequences (for example, the Catalan and Motzkin numbers) may be expressed as the constant term of , for some Laurent polynomials and i…
Explicit Expressions for the Variance and Higher Moments of the Size of a Simultaneous Core Partition and its Limiting Distribution
Shalosh B. Ekhad, Doron Zeilberger
Jaclyn Anderson proved that if s and t are relatively prime positive integers, then there are exactly (s+t-1)!/(s!t!) partitions whose set of hook-lengths is disjoint from the set…