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

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

2005-06-23

arxiv.org/abs/math/0506466v4

Math. Intelligencer 31 (2009), no. 1, 9--17.

Mathematics

Combinatorics

Small revisions, added references

Scientific paper

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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