Abstract:The notion of Ehrhart tensor polynomials, a natural generalization of the Ehrhart polynomial of a lattice polytope, was recently introduced by Ludwig and Silverstein. We initiate a study of their coefficients. In the vector and matrix cases, we give Pick-type formulas in terms of triangulations of a lattice polygon. As our main tool, we introduce h r -tensor polynomials, extending the notion of the Ehrhart h * -polynomial, and, for matrices, investigate their coefficients for positive semidefiniteness. In cont… Show more
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