### 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 language | English |
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Pages (from-to) | 1-8 |

Journal | Münster Journal of Mathematics |

Volume | 1 |

Publication status | Published - 2008 |

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## Cite this

Cohen, A. M. (2008). Eulerian polynomials of spherical type.

*Münster Journal of Mathematics*,*1*, 1-8.