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


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.

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