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Weighted Ehrhart theory

Algebra & Discrete Mathematics

Speaker: Alan Stapledon, MSRI
Location: 2112 MSB
Start time: Fri, Oct 9 2009, 4:10PM

Motivated by geometry, we introduced a purely combinatorial integration theory which takes a lattice polytope P and a piecewise linear function λ and outputs a power series \tilde{h}*(P, λ) ∈ \mathbb{Z}[[t1/N]], for some positive integer N. We prove a change of variables formula relating these 'integrals' on different lattice polytopes, and, in the case when λ is identically zero, we show how \tilde{h}*(P, 0) reveals some hidden symmetry in the Ehrhart h*-vector of P.