Let
R
R
be the face ring of a simplicial complex of dimension
d
−
1
d-1
and
R
(
n
)
{\mathcal R}({\mathfrak {n}})
be the Rees algebra of the maximal homogeneous ideal
n
{\mathfrak {n}}
of
R
.
R.
We show that the generalized Hilbert-Kunz function
H
K
(
s
)
=
ℓ
(
R
(
n
)
/
(
n
,
n
t
)
[
s
]
)
HK(s)=\ell ({\mathcal {R}}({\mathfrak {n}})/({\mathfrak {n}}, {\mathfrak {n}} t)^{[s]})
is given by a polynomial for all large
s
.
s.
We calculate it in many examples and also provide a Macaulay2 code for computing
H
K
(
s
)
.
HK(s).