5 papers · 1 filter
Bergeron's conjecture & a tale of two binomial coefficients
Tewodros Amdeberhan, Matthias Beck
Bergeron's conjecture states that, if are integers with , then one has the coefficient-wise inequality among two Gaus…
Sprout Symmetric Functions: Part 1
Tewodros Amdeberhan, John Shareshian, Richard P. Stanley
A \emph{sprout sequence} is a sequence $\frakr=(R_0=1,R_1,R_2,\dots)$ of symmetric functions in the variables $\bmx=(x_1,x_2,\dots)$ over a field generated from a power series…
The Challenge of Computing Geode Numbers
Tewodros Amdeberhan, Manuel Kauers, Doron Zeilberger
In a fascinating recent American Mathematical Monthly article, Norman Wildberger and Dean Rubine introduced a new kind of combinatorial numbers, that they aptly named the ``Geode n…
Proofs Of Three Geode Conjectures
Tewodros Amdeberhan, Doron Zeilberger
In the May 2025 issue of the Amer. Math. Monthly, Norman J. Wildberger and Dean Rubine intoduced a new kind of multi-indexed numbers, that they call `Geode numbers', obtained from…
Hook lengths in self-conjugate partitions
Tewodros Amdeberhan, George E. Andrews, Ken Ono +1
In 2010, G.-N. Han obtained the generating function for the number of size hooks among integer partitions. Here we obtain these generating functions for self-conjugate partitio…