\(q\)-Eulerian polynomials arising from Coxeter groups. (English) Zbl 0809.05012

Brenti, Francesco

Eur. J. Comb. 15, No. 5, 417-441 (1994).

The author generalizes the classical Eulerian numbers and Eulerian polynomials by the enumeration of a finite Coxeter system with respect to the number of descents. Natural \(q\)-analogues are given. The results are relevant for computing Betti numbers of certain toric projective varieties.

Reviewer: L.A.Székely (Budapest)

MSC:

05A30	\(q\)-calculus and related topics
05A15	Exact enumeration problems, generating functions
05E10	Combinatorial aspects of representation theory
11B68	Bernoulli and Euler numbers and polynomials
20F55	Reflection and Coxeter groups (group-theoretic aspects)

Keywords:

Coxeter groups; Eulerian numbers; Eulerian polynomials; enumeration; Betti numbers