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Theorems of Brion, Lawrence, and Varchenko on rational generating functions for cones

Matthias Beck·Christian Haase·Frank Sottile
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Abstract

We discuss and give elementary proofs of results of Brion and of Lawrence-Varchenko on the lattice-point enumerator generating functions for polytopes and cones. This largely expository note contains a new proof of Brion's Formula using irrational decompositions, and a generalization of the Lawrence-Varchenko formula.

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Matthias Beck, Christian Haase, Frank Sottile. 2008-03-22. Theorems of Brion, Lawrence, and Varchenko on rational generating functions for cones. https://arxiv.org/abs/math/0506466

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