Brenti, Francesco \(q\)-Eulerian polynomials arising from Coxeter groups. (English) Zbl 0809.05012 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) Cited in 8 ReviewsCited in 76 Documents 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 PDF BibTeX XML Cite \textit{F. Brenti}, Eur. J. Comb. 15, No. 5, 417--441 (1994; Zbl 0809.05012) Full Text: DOI