Related Topics
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
Famous quotes containing the word related:
“Just as a new scientific discovery manifests something that was already latent in the order of nature, and at the same time is logically related to the total structure of the existing science, so the new poem manifests something that was already latent in the order of words.”
—Northrop Frye (b. 1912)
“A parent who from his own childhood experience is convinced of the value of fairy tales will have no difficulty in answering his childs questions; but an adult who thinks these tales are only a bunch of lies had better not try telling them; he wont be able to related them in a way which would enrich the childs life.”
—Bruno Bettelheim (20th century)