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A branch of geometry dealing with convex sets and functions. Polytopes, convex bodies, discrete geometry, linear programming, antimatroids, ...

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The number of hyperplanes determining the integer points of a polyhedron

The answer to both your questions is Gomory cuts. From a non-interger extreme point $x$ of $P$ it is easy to find an hyperplane $H$ which separate $x$ from $Int(P)$. Such an hyperplane is called a Gom …
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