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The possible sign patterns of the coefficients of Ehrhart polynomialsAlgebra & Discrete Mathematics
The Ehrhart polynomial of an integral convex polytopes
counts lattice points under dilations of the polytopes.
In this talk I will discuss the possible sign patterns of the
coefficients of Ehrhart polynomials.
While the leading terms, the second leading terms and the constant of
Ehrhart polynomials are always positive,
the other terms aren't necessarily positive and few examples of
Ehrhart polynomials with negative coefficients were
known before. I will describe a construction of Ehrhart polynomials
with various sign patterns.