Alternating Eulerian polynomials and left peak polynomials
Abstract
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 polynomials have gamma-vectors alternate in sign.
- Publication:
-
arXiv e-prints
- Pub Date:
- April 2021
- DOI:
- 10.48550/arXiv.2104.09374
- arXiv:
- arXiv:2104.09374
- Bibcode:
- 2021arXiv210409374M
- Keywords:
-
- Mathematics - Combinatorics;
- 05A05
- E-Print:
- 12 pages