There is a long tradition of using polytopes to understand polynomials of importance in algebraic combinatorics. For example, the Kostka numbers equal the number of lattice points in the Gelfand–Tsetlin polytopes. In this talk I will give an overview of this connection. We will discuss sums of weighted lattice points of polytopes and show that they can be computed as sums of unweighted lattice points of polytopes. As a consequence, we obtain a computational tool to estimate the maximal weighted lattice point in a polytope. This is based on joint work with De Loera, Kaplan, and Wang.
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