(Formulas of Brion, Lawrence, and Varchenko on rational generating functions for cones)

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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