On the Eulerian polynomials of type D

Authors:
Chak-On Chow
Affiliations:
Institute of Mathematics, Academia Sinica, Taipei 11529, Taiwan
Venue:
European Journal of Combinatorics
Year:
2003

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Abstract

We define and study sub-Eulerian polynomials of type D , which count the elements of the group of even-signed permutations D n with respect to the number of descents in a refined sense. The recurrence relations and exponential generating functions of the sub-Eulerian polynomials are determined, by which the solution to a problem of Brenti, concerning the recurrence relation for the Eulerian polynomials of type D , is also obtained.