5 papers
Estimating Many Constants With a Coin
Shalosh B. Ekhad, Doron Zeilberger
We extend, and fully implement, in Maple, Jim Propp's charming way of estimating Pi via tossing a fair coin, and compute many other constants, even going beyond the far more genera…
Experimenting with the Garsia-Milne Involution Principle
Shalosh B. Ekhad, Doron Zeilberger
In 1981, Adriano Garsia and Steve Milne found the first bijective proof of the celebrated Rogers-Ramanujan identities. To achieve this feat, they invented a versatile tool that the…
Efficient Weighted Counting of Multiset Derangements
Shalosh B. Ekhad, Doron Zeilberger
We use the Almkvist-Zeilberger algorithm, combined with a weighted version of the Even-Gillis Laguerre integral due to Foata and Zeilberger, in order to efficiently compute weight…
Automated Generation of Generating Functions Related to Generalized Stern's Diatomic Arrays in the footsteps of Richard Stanley
Shalosh B. Ekhad, Doron Zeilberger
Using Symbolic Dynamic Programming we describe algorithms, fully implemented in Maple, for automatically generating generating functions introduced by Richard Stanley in his study…
The Asymptotic expansion of OEIS sequence A85
Shalosh B. Ekhad, Manuel Kauers, Doron Zeilberger
One of the most important sequences in enumerative combinatorics is OEIS sequence A85, the number of involutions of length n. In the Art of Computer Programming, vol. 3, Don Knuth…