Combinatorics Seminar 2018


Speaker: Jiang Zeng (曾江), Université Claude Bernard Lyon-I

Date: Mon, May 14, 2018

Time: 16:00 - 17:00

Venue: Middle Meeting Room

Title: How to generalize Eulerian polynomials via combinatorics and continued fractions

Abstract:

One of the interesting aspects of Eulerian polynomials is the characterization as the moments of orthogonal Meixner polynomials. Motivated by the problems of tatal positivity and gamma-positivity of combinatorial polynomial sequences, I will present two recent generalizations from this perspective. Firstly we show a $q$-exponential generating function for Carlitz-Scoville’s polynomials using inversion numbers of permutations. Secondly we find Stieltjes-type and Jacobi-type continued fractions for some master Eulerian polynomials that enumerate permutations. Our results contain many previously obtained identities as special cases.

Slides: View slides


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