  Let $R$ be a commutative ring with identity and let $V$ be a free $R$-module
of rank $n$ for some $n\in\mathbb{N}$. Fixing an $R$-basis $\mathcal{E}$ of
$V$, the symmetric group $\mathfrak{S}_n$ acts on $V$ by permuting
$\mathcal{E}$ and hence on tensor space $V^{\otimes r}$ for $r\in\mathbb{N}$
via the usual tensor product action turning $V$ and $V^{\otimes r}$ into
$R\mathfrak{S}_n$-modules. For units $q$ in $R$ we construct an action of the
corresponding Iwahori-Hecke algebra $\mathcal{H}_{R,q}(\mathfrak{S}_n)$ which
specializes to the action of $R\mathfrak{S}_n$, if $q$ is taken to $1$. The
centralizing algebra of this action is called the $q$-partition algebra
$\mathcal{P}_{R,q}(n,r)$. Let $R$ be a field of characteristic not dividing
$q$. We prove, that $\mathcal{P}_{R,q}(n,r)$ is isomorphic to the $q$-partition
algebra defined by Halverson and Thiem by different means a few years ago.
