On a theorem of Brion

Details On a theorem of Brion On a theorem of Brion

2006-07-12

arxiv.org/abs/math/0607297v2

Mathematics

Combinatorics

11 pages, 3 figures; v2: references updated, minor typos corrected

Scientific paper

We give an elementary geometric re-proof of a formula discovered by Michel Brion as well as two variants thereof. A subset of R^n gives rise to a formal Laurent series with monomials corresponding to lattice points in the set. Under suitable hypotheses, these series represent rational functions. We will prove formulae relating the rational function of a lattice polytope P to the sum of rational functions corresponding to the supporting cones subtended at the vertices of P. The exposition should be suitable for everyone with a little background in topology.

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