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McMullen's formulas for Ehrhart coefficients

Algebra & Discrete Mathematics

Speaker: Maren Ring, University of Rostock
Related Webpage: https://www.geometrie.uni-rostock.de/people/maren/
Location: 1147 MSB
Start time: Mon, Apr 16 2018, 3:10PM

The Ehrhart polynomial counts the number of lattice points in dilates of a polytope and gives us a useful connection between volumes and discrete points. Determining the coefficients of this polynomial can be done via so-called McMullen's formulas (aka local formulas), which give the i-th coefficient as a weighted sum of the volumes of the i-dimensional faces of the polytope.

Based on choices of lattice tiles we construct a new local formula that provides us with additional knowledge about Ehrhart coefficients and can be used for the exploitation of polyhedral symmetries. This is joint work with A. Schürmann.