Eulerian polynomials of spherical type

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Abstract

The Eulerian polynomial of a finite Coxeter system (W, S) of rank n records, for each k ¿ {1, . . . , n}, the number of elements w ¿ W with an ascent set {s ¿ S | l(ws) > l(w)} of size k, where l(w) denotes the length of w with respect to S. The classical Eulerian polynomial occurs when the Coxeter group has type An, so W is the symmetric group on n + 1 letters. Victor Reiner gave a formula for arbitrary Eulerian polynomials and showed how to compute them in the classical cases. In this note, we compute the Eulerian polynomial for any spherical type.
Original languageEnglish
Pages (from-to)1-8
JournalMünster Journal of Mathematics
Volume1
Publication statusPublished - 2008

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