Séminaire Lotharingien de Combinatoire, 84B.40 (2020), 12 pp.
Bin Han, Jianxi Mao and Jiang Zeng
Eulerian Polynomials and Excedance Statistics Via Continued Fractions
It is well known that
the permutation peak polynomials and descent polynomials are connected
via a quadratic transformation. By rephrasing the latter formula with
permutation cycle peaks and excedances
we are able to prove a series of general formulas expressing polynomials counting permutations by various excedance statistics in terms of refined Eulerian polynomials.
Received: November 20, 2019.
Accepted: February 20, 2020.
Final version: April 30, 2020.
The following versions are available: