Theorem 1
(Harper’s Theorem)
.
Assuming that:
A
⊂
Q
n
C
the initial segment of
simplicial ordering
with
|
C
|
=
|
A
|
Then
|
N
(
A
)
|
≥
|
N
(
C
)
|
. In particular, if
|
A
|
=
∑
i
=
0
r
n
i
then
|
N
(
A
)
|
≥
∑
i
=
0
r
+
1
n
i
.