  Let $p_{-t}(n)$ denote the number of partitions of $n$ into $t$ colors. In
analogy with Ramanujan's work on the partition function, Lin recently proved in
\cite{Lin} that $p_{-3}(11n+7)\equiv0\pmod{11}$ for every integer $n$. Such
congruences, those of the form $p_{-t}(\ell n + a) \equiv 0 \pmod {\ell}$, were
previously studied by Kiming and Olsson. If $\ell \geq 5$ is prime and $-t \not
\in \{\ell - 1, \ell -3\}$, then such congruences satisfy $24a \equiv -t \pmod
{\ell}$. Inspired by Lin's example, we obtain natural infinite families of such
congruences. If $\ell\equiv2\pmod{3}$ (resp. $\ell\equiv3\pmod{4}$ and
$\ell\equiv11\pmod{12}$) is prime and $r\in\{4,8,14\}$ (resp. $r\in\{6,10\}$
and $r=26$), then for $t=\ell s-r$, where $s\geq0$, we have that
\begin{equation*} p_{-t}\left(\ell
n+\frac{r(\ell^2-1)}{24}-\ell\Big\lfloor\frac{r(\ell^2-1)}{24\ell}\Big\rfloor\right)\equiv0\pmod{\ell}.
\end{equation*} Moreover, we exhibit infinite families where such congruences
cannot hold.
