Lattice-points enumeration in polytopes : study of the coefficients of the Ehrhart quasi-polynomial
A very important problem in discrete geometry is counting points with integer-coordinates (also called "lattice-points") in polytopes. A polytope is a geometric shape that is the smallest convex set containing the vertices defining the polytope. For instance, in two dimensions, a polytope would simply be a convex polygon. Lattice-point enumeration has applications in a lot of different areas of mathematics, including combinatorics and operations research. Our goal is to study the function that counts the lattice-points in a polytope and its integer dilates when the vertices of the polytope have ...
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