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The case n = d = 2 and t = 1 of these statements yields Pick's theorem. Formulas for the other coefficients are much harder to get; Todd classes of toric varieties, the Riemann–Roch theorem as well as Fourier analysis have been used for this purpose.
If X is the toric variety corresponding to the normal fan of P, then P defines an ample line bundle on X, and the Ehrhart polynomial of P coincides with the Hilbert polynomial of this line bundle.
Read more about this topic: Ehrhart Polynomial
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