Euler numbers and André Permutations


Topic: Euler numbers and André Permutations

Speaker: Professor Zeng Jiang

Event date: 12/2/2019

Event time: 9:00 am

Venue: Lecture Hall 1506

Sponsor: School of Mathematics and Statistics, Institute of Science and Technology


The Euler numbers are the coeffcients in the Taylor expansion of tan x+sec x. A classical result of Andre says that these coeffcients enumerate alternating permutations. In the 1970's Foata and Shcutzenberger found another family of permutations, called Andre permutations,also enumerated by Euler numbers and proved that the descent polynomials of Andre permutations are related to the gamma-coeffcients of Eulerianpolynomials. In this talk, I will present a (p; q)-analogue of their resultusing the combinatorial theory of continued fractions, which gives a satisfactory answer to a conjecture of Branden on the gamma-coeffcients of his(p; q)-analogue of Eulerian polynomials. In particular, this answers a recent question of G.N. Hanon his q-Euler numbers