Séminaire Lotharingien de Combinatoire, 84B.40 (2020), 12 pp.

Bin Han, Jianxi Mao and Jiang Zeng

Eulerian Polynomials and Excedance Statistics Via Continued Fractions

Abstract. 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.

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