1 citations · 2 across the 5 of their papers we have counts for
6 papers
The Generating Function of Ternary Trees and Continued Fractions
Ira Gessel, Guoce Xin
Michael Somos conjectured a relation between Hankel determinants whose entries count ternary trees and the number of certain plane partitions and alterna…
A Short Proof of the Zeilberger-Bressoud -Dyson Theorem
Ira M. Gessel, Guoce Xin
We give a formal Laurent series proof of Andrews's -Dyson Conjecture, first proved by Zeilberger and Bressoud.
A triple lacunary generating function for Hermite polynomials
Ira M. Gessel, Pallavi Jayawant
Some of the classical orthogonal polynomials such as Hermite, Laguerre, Charlier, etc. have been shown to be the generating polynomials for certain combinatorial objects. These com…
Signed Mahonians
Ron M. Adin, Ira M. Gessel, Yuval Roichman
A classical result of MacMahon gives a simple product formula for the generating function of major index over the symmetric group. A similar factorial-type product formula for the…
The polynomial part of a restricted partition function related to the Frobenius problem
Matthias Beck, Ira M. Gessel, Takao Komatsu
Given a set of positive integers A = {a_1,...,a_n}, we study the number p_A (t) of nonnegative integer solutions (m_1,...,m_n) to m_1 a_1 + ... m_n a_n = t. We derive an explicit f…
Enumeration of tilings of diamonds and hexagons with defects
Harald Helfgott, Ira M. Gessel
We show how to count tilings of Aztec diamonds and hexagons with defects using determinants. In several cases these determinants can be evaluated in closed form. In particular, we…