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The possible sign patterns of the coefficients of Ehrhart polynomials

Algebra & Discrete Mathematics

Speaker: Akiyoshi Tsuchiya, Osaka U
Related Webpage: https://www.researchgate.net/profile/Akiyoshi_Tsuchiya
Location: 1147 MSB
Start time: Mon, Feb 1 2016, 1:10PM

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.