# Ehrhart polynomial

Let Δ be an

integral convex polytope of

dimension *n* in a

lattice *M*, and let

*l*_{Δ}(

*k*) be the number of lattice points in Δ dilated by a factor of the

integer *k*,

- .

Then

*l*_{Δ}(

*k*) can be shown to be an

*n*th-degree

polynomial with

rational coefficients in

*k*, called the

**Ehrhart polynomial** of the polytope Δ: