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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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