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Chris O'Neill : An Introduction to Ehrhart Theory and Lattice Point Enumeration

A polytope is a bounded subset of R^d which is the intersection of finitely many half-spaces. Given a polytope P, we can consider integer dilations of P, and ask how many integer points are contained in each dilation, as a function of the dilation factor. Under the right conditions, this counting function is a polynomial with some very interesting and unexpected properties. To demonstrate the usefulness of these results, we will give alternative proofs to some well known results from far outside the realm of geometry.

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