91 citations · 520 across the 230 of their papers we have counts for
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Automatic Solution of Richard Stanley's Amer. Math. Monthly Problem #11610 and ANY Problem of That Type
Shalosh B. Ekhad, Doron Zeilberger
Richard Stanely proposed, in a recent Amer. Math. Monthly Problem, to prove a nice explicit formula for the generating function for the number of n-letter words in {H,T} that have…
How to Gamble If You're In a Hurry
Shalosh B. Ekhad, Doron Zeilberger
The beautiful theory of statistical gambling, started by Dubins and Savage (for subfair games) and continued by Kelly and Breiman (for superfair games) has mostly been studied unde…
Rademacher's infinite partial fraction conjecture is (almost certainly) false
Andrew V. Sills, Doron Zeilberger
In his book \emph{Topics in Analytic Number Theory}, Hans Rademacher conjectured that the limits of certain sequences of coefficients that arise in the ordinary partial fraction de…
Alexander Burstein's Lovely Combinatorial Proof of John Noonan's Beautiful Formula that the number of n-permutations that contain the Pattern 321 Exactly Once Equals (3/n)(2n)!/((n-3)!(n+3)!)
Doron Zeilberger
In 1996, my brilliant student John Noonan, discovered, and proved that there are 3(2n)!/(n(n+3)!(n-3)!) ways to line-up n people of different heights in such a way that out of the…
Formulae for the number of partitions of n into at most m parts (using the quasi-polynomial ansatz)
Andrew V. Sills, Doron Zeilberger
The purpose of this short article is to announce, and briefly describe, a Maple package, PARTITIONS, that (inter alia) completely automatically discovers, and then proves, explicit…
The Discrete Analog of the Malgrange-Ehrenpreis Theorem
Doron Zeilberger
One of the landmarks of the modern theory of partial differential equations is the Malgrange- Ehrenpreis theorem that states that every non-zero linear partial differential operato…