Theorems of Brion, Lawrence, and Varchenko on rational generating functions for cones
classification
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brionconesformulafunctionsgeneratinglawrence-varchenkocontainsdecompositions
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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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