I. Gessel

collaborators

3 papers

math.CO2025

Lattice paths and the Geode

Ira M. Gessel

Let $t_{1}, t_{2}, \dots$ be variables, and let $S$ be the formal power series in the variables $t_{1}, t_{2}, \dots$ satisfying $S = 1 + \sum_{i = 1}^{\infty} t_{n} S^{n} .$ Let $S_1 =\sum_{n=1}^\infty t…

math.CO2024

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…

math.CO2024

Two-sided permutation statistics via symmetric functions

Ira M. Gessel, Yan Zhuang

Given a permutation statistic $st$ , define its inverse statistic $ist$ by $ist (I ¨ ) := st (I ¨ ^{- 1})$ . We give a general appr…