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

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)
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