6 citations · 8 across the 9 of their papers we have counts for
6 papers · 1 filter
The Mahonian probability distribution on words is asymptotically normal
E. Rodney Canfield, Svante Janson, Doron Zeilberger
The Mahonian statistic is the number of inversions in a permutation of a multiset with elements of type , . The counting function for this statistic is the $q…
Some Nice Sums are Almost as Nice if you turn them Upside Down
Moa Apagodu, Doron Zeilberger
We represent the sums , , $\sum_{k=0}^{n-1}\frac{q^{-k(k-1)}}{{\genfrac{[}{]}{0pt}{}{n}{k}}_q}…
Finite Analogs of Szemerédi's Theorem
Paul Raff, Doron Zeilberger
One of the "deepest" theorems in mathematics is Endre Szemerédi's theorem about the inevitability of arithmetical progressions. Here we try to nibble at it, by doing "finite" analo…
A Symbolic Computational Approach to a Problem Involving Multivariate Poisson Distributions
Eduardo Sontag, Doron Zeilberger
Multivariate Poisson random variables subject to linear integer constraints arise in several application areas, such as queuing and biomolecular networks. This note shows how to co…
Teaching the Computer how to Discover(!) and then Prove(!!) (all by Itself(!!!)) Analogs of Collatz's Notorious 3x+1 Conjecture
Doron Zeilberger
Paul Erdos claimed that mathematics is not yet ready to settle the 3x+1 conjecture. I agree, but very soon it will be! With the exponential growth of computer-generated mathematics…
On the number of walks on a regular Cayley tree
Eric Rowland, Doron Zeilberger
We provide a new derivation of the well-known generating function counting the number of walks on a regular tree that start and end at the same vertex, and more generally, a genera…