We first present grammatical interpretations for the alternating Eulerian polynomials of types A and B. As applications, we then derive several properties of the type B alternating Eulerian polynomials, including recurrence relations, generating function and unimodality. And then, we establish an interesting connection between alternating Eulerian polynomials of type B and left peak polynomials, which implies that the type B alternating Eulerian polynomials have gamma-vectors that alternate in sign.
Bibliographical noteFunding Information:
This work is supported by NSFC 12071063 . The authors appreciate the careful review, corrections and helpful suggestions to this paper made by the referees.
© 2021 Elsevier B.V.
- Alternating descents
- Eulerian polynomials
- Left peaks
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics