Let s, t be natural numbers and fix an s-core partition $$\sigma $$
σ
and a t-core partition $$\tau $$
τ
. Put $$d=\gcd (s,t)$$
d
=
gcd
(
s
,
t
)
and $$m={{\,\textrm{lcm}\,}}(s,t)$$
m
=
lcm
(
s
,
t
)
, and write $$N_{\sigma , \tau }(k)$$
N
σ
,
τ
(
k
)
for the number of m-core partitions of length no greater than k whose s-core is $$\sigma $$
σ
and t-core is $$\tau $$
τ
. We prove that for k large, $$N_{\sigma , \tau }(k)$$
N
σ
,
τ
(
k
)
is a quasipolynomial of period m and degree $$\frac{1}{d}(s-d)(t-d)$$
1
d
(
s
-
d
)
(
t
-
d
)
.