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arXiv · 1206.1551

Lattice Point Generating Functions and Symmetric Cones

Matthias Beck·Thomas Bliem·Benjamin Braun·Carla Savage
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Abstract

We show that a recent identity of Beck-Gessel-Lee-Savage on the generating function of symmetrically contrained 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 the specific cases of a symmetry group of type A (previously known) and types B and D (new). We obtain several applications of the special cases in type B, including identities involving permutation statistics and lecture hall partitions.

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Matthias Beck, Thomas Bliem, Benjamin Braun, Carla Savage. 2012-06-07. Lattice Point Generating Functions and Symmetric Cones. https://doi.org/10.1007/s10801-012-0414-9

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