86 citations · 231 across the 46 of their papers we have counts for
50 papers
Lattice paths and the Geode
Ira M. Gessel
Let be variables, and let be the formal power series in the variables satisfying Let $S_1 =\sum_{n=1}^\infty t…
Counting up-up-or-down-down permutations
Ira M. Gessel
Answering a question of Donald Knuth, we find the bivariate exponential generating function for "up-up-or-down-down'' permutations of odd length according to their last entry. An u…
A short proof of the Almkvist-Meurman theorem
Ira M. Gessel
We give a short generating function proof of the Almkvist-Meurman theorem: For integers and , define the numbers by $kx(e^{hx}-1)/(e^{kx}-1)=\sum_{n=0}^\infty…
Two-sided permutation statistics via symmetric functions
Ira M. Gessel, Yan Zhuang
Given a permutation statistic , define its inverse statistic by . We give a general approa…
Good Will Hunting's Problem: Counting Homeomorphically Irreducible Trees
Ira M. Gessel
In the film Good Will Hunting, the main character, a janitor at MIT named Will Hunting, attacks the problem of drawing all the homeomorphically irreducible trees with 10 vertices.…
Binomial convolutions for rational power series
Ira M. Gessel, Ishan Kar
The binomial convolution of two sequences and is the sequence whose th term is . If and have rat…