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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}[[t^{1/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.