I am reading a research paper in which following equation is given: $\underset{\small{X}\\\text{s.t}\sum_{(i,k)\in \mathcal{A}}x_{ik}=1, \forall i\in \mathcal{M}}{\operatorname{max}} u$
where $\small{X}$ is a binary variable that collects all $x_{i,k}$
$\mathcal{M}$ is a set of clients and say its elements are $\mathcal{M} = \{1,2,3,4\}$,
$k$ denotes the node such that $k = \{1,2\}$ i.e., there are two nodes and four clients in the system.
$\mathcal{A}$ is a set of all possible combination of node and client, so there will be 8 elements in it and is given by $\mathcal{A} = \{(1,1),(2,1),(3,1),(4,1),(1,2),(2,2),(3,2),(4,2)\}$.
$u = \sum_{(i,k)\in \mathcal{A}}a_{ik}x_{ik}$ and let say $a_{ik} = 1$ for simplicity.
Also $\mathcal{S}$ is a subset of $\mathcal{A}$ such that $x_{i,k}=1$ if $(i,k)\in \mathcal{S}$ and $x_{i,k}=0$ otherwise, for all $(i,k)\in \mathcal{A}$.
My query is how the such that expression will be equal to one.
Any help in this regard will be highly appreciated.
