Introductory Workshop: Geometric and Topological Combinatorics September 05, 2017 - September 08, 2017
Location: MSRI: Simons Auditorium
05A15 - Exact enumeration problems, generating functions [See also 33Cxx, 33Dxx]
52B20 - Lattice polytopes (including relations with commutative algebra and algebraic geometry) [See also 06A11, 13F20, 13Hxx]
52B45 - 'Dissections and valuations (Hilbert''s third problem, etc.)'
We say a polytope is Ehrhart positive if its Ehrhart polynomial has positive coefficients. There are different examples of polytopes shown to be Ehrhart positive using different techniques. We will survey some of these results. Through work of Danilov/McMullen, there is an interpretation of Ehrhart coefficients relating to the normalized volumes of faces. We try to make this relation more explicit in the particular case of the regular permutohedron. The goal is to prove Ehrhart positivity for generalized permutohedra. If time permits, I will also discuss some related questions. This is joint work with Federico Castillo.
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