Alternating Eulerian polynomials and left peak polynomials

Shi Mei Ma, Qi Fang, Toufik Mansour, Yeong Nan Yeh

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Article number112714
JournalDiscrete Mathematics
Issue number3
StatePublished - Mar 2022

Bibliographical note

Funding 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.

Publisher Copyright:
© 2021 Elsevier B.V.


  • Alternating descents
  • Eulerian polynomials
  • Gamma-vectors
  • Left peaks

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


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