Séminaire Lotharingien de Combinatoire, 80B.57 (2018), 12 pp.

Arthur Nunge

Eulerian Polynomials on Segmented Permutations

Abstract. We define a generalization of the Eulerian polynomials and the Eulerian numbers by considering a descent statistic on segmented permutations coming from the study of 2-species exclusion processes and a change of basis in a Hopf algebra. We give some properties satisfied by these generalized Eulerian numbers. We also define a q-analog of these Eulerian polynomials which gives back usual Eulerian polynomials and ordered Bell polynomials for specific values of its variables. We also define a noncommutative analog living in the algebra of segmented compositions. It gives us an explicit generating function and some identities satisfied by the generalized Eulerian polynomials such as a Worpitzky-type relation.


Received: November 14, 2017. Accepted: February 17, 2018. Final version: April 1, 2018.

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