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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: