91 citations · 520 across the 230 of their papers we have counts for
8 papers · 1 filter
On the Asymptotic Statistics of the Number of Occurrences of Multiple Permutation Patterns
Svante Janson, Brian Nakamura, Doron Zeilberger
We study statistical properties of the random variables , the number of occurrences of the pattern in the permutation . We present two contrasting approaches to this…
A Case Study in Meta-AUTOMATION: AUTOMATIC Generation of Congruence AUTOMATA For Combinatorial Sequences
Eric Rowland, Doron Zeilberger
This article is a sequel to a recent article by Eric Rowland and Reem Yassawi, presenting yet another approach to the fast determination of congruence properties of `famous' combin…
How to Extend Karolyi and Nagy's BRILLIANT Proof of the Zeilberger-Bressoud q-Dyson Theorem in order to Evaluate ANY Coefficient of the q-Dyson Product
Shalosh B. Ekhad, Doron Zeilberger
We show how to extend the Karolyi-Nagy beautiful proof of the Zeilberger-Bressoud q-Dyson theorem, (first proved by Zeilberger and Bressoud in 1985, and originally conjectured by G…
Generalizing and Implementing Michael Hirschhorn's Amazing Algorithm for Proving Ramanujan-Type Congruences
Edinah Gnang, Doron Zeilberger
When Mike Hirschhorn showed us his lovely gem, that gives the simplest-to-date proof of Ramanujan's famous result that p(11n+6) is divisible by 11, we realized that his amazing met…
A Short Proof of a Ptolemy-Like Relation for an Even number of Points on a Circle Discovered by Jane McDougall
Marc Chamberland, Doron Zeilberger
We give a short proof of a Ptolemy-style result first discovered and proved by Jane McDougall. It may be viewed as a generalization to any even number of points of the cubic relati…
On Euler's "Misleading Induction", Andrews' "Fix", and How to Fully Automate them
Shalosh B. Ekhad, Doron Zeilberger
One of the greatest experimental mathematicians of all time was also one of the greatest mathematicians of all time, the great Leonhard Euler. Usually he had an uncanny intuition o…