Enumerative combinatorics
Permutation statistics of indexed permutations
European Journal of Combinatorics
q-Eulerian polynomials arising from Coxeter groups
European Journal of Combinatorics
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We show that a recent identity of Beck---Gessel---Lee---Savage on the generating function of symmetrically constrained compositions of integers generalizes naturally to a family of convex polyhedral cones that are invariant under the action of a finite reflection group. We obtain general expressions for the multivariate generating functions of such cones, and work out their general form more specifically for all symmetry groups of type A (previously known) and types B and D (new). We obtain several applications of these expressions in type B, including identities involving permutation statistics and lecture hall partitions.