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Maren Helene Ring

Local formulas for Ehrhart coefficients from lattice tiles

Universität Rostock, 2019

Abstract: The coefficients of the Ehrhart polynomial of a lattice polytope can be written as a weighted sum of facial volumes. The weights in such a 'local formula' depend only on the outer normal cones of faces, but are far from being unique. In this thesis, we present local formulas μ based on choices of fundamental domains that, which allows a geometric interpretation of the values. Additionally, we generalize the results to Ehrhart quasipolynomials, prove new results about the symmetric behavior and introduce a variation well-suited for implementations.

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