Geodesic
Lattice point generating functions and symmetric cones
Journal of Algebraic Combinatorics, Tome 38 (2013) no. 3, pp. 543-566.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Keywords: lattice point generating function, polyhedral cone, finite reflection group, Coxeter group, symmetrically constrained composition, permutation statistics, lecture Hall partition 
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     title = {Lattice point generating functions and symmetric cones},
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Beck, Matthias; Bliem, Thomas; Braun, Benjamin; Savage, Carla D. Lattice point generating functions and symmetric cones. Journal of Algebraic Combinatorics, Tome 38 (2013) no. 3, pp. 543-566. http://geodesic.mathdoc.fr/item/JAC_2013__38_3_a8/