Let
I
⊂
S
=
K
,
[
x
1
,
…
,
x
n
]
I\subset S=\mathbb {K},[x_1,\dots ,x_n]
be an ideal generated by squarefree monomials of degree
≥
d
\ge d
. If the number of degree
d
d
minimal generating monomials is
μ
d
(
I
)
≤
min
(
(
n
d
+
1
)
,
∑
j
=
1
n
−
d
(
2
j
−
1
j
)
)
\mu _d(I)\le \min (\binom {n}{d+1},\sum _{j=1}^{n-d}\binom {2j-1}{j})
, then the Stanley depth
sdepth
S
(
I
)
≥
d
+
1
\operatorname {sdepth}_S(I)\ge d+1
.