Alternating Eulerian polynomials and left peak polynomials

@article{Ma2022AlternatingEP,
  title={Alternating Eulerian polynomials and left peak polynomials},
  author={Shi-Mei Ma and Qi Fang and Toufik Mansour and Yeong-Nan Yeh},
  journal={Discrete Mathematics},
  year={2022}
}
In this paper we present grammatical interpretations of the alternating Eulerian polynomials of types A and B. As applications, we derive several properties of the type B alternating Eulerian polynomials, including combinatorial expansions, recurrence relations and generating functions. We establish an interesting connection between alternating Eulerian polynomials of type B and left peak polynomials of permutations in the symmetric group, which implies that the type B alternating Eulerian… Expand

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