Ehrhart polynomial
Let Δ be an
integral convex polytope of
dimension n in a
lattice M, and let
lΔ(
k) be the number of lattice points in Δ dilated by a factor of the
integer k,
- .
Then
lΔ(
k) can be shown to be an
nth-degree
polynomial with
rational coefficients in
k, called the
Ehrhart polynomial of the polytope Δ: