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Let $N = \{1,2,3,4\}, T=\{1,2,3,4,5,6\}$ and let $i,j \in N$.

I am trying to understand what the following sum means but am having a little difficulty in comprehending it:

$$\sum_{j \in N \setminus \{i\}} (x_{i,j,t} + x_{j,i,t}) = 1 \qquad \forall i \in N, t \in T$$

Would someone be able to give me an example of what a few iterations of this would look like? I am having trouble wrapping my head around it.

Edit: To help clarify the context, this is supposed to read as: $x_{i,j,t}$ is a game between team $i$ and $j$ at time $t$, at team $i$'s home stadium.

The sum is supposed to read as: "Each team $i$ plays exactly once per period $t$."

mathplzfun
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    $N\setminus {i}$ N\setminus \{i\} – peterwhy Jun 26 '21 at 15:25
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    This is a constraint for each $i \in N$ and $t \in T$. You should try picking two specific values and see if you can rewrite the constraint. For example, if $i=1$ and $t=1$, what would $N\setminus {1}$ equal? And what would the equation be? – Joe Jun 26 '21 at 15:28
  • For team i, the sum is over all other teams (N is the set of teams). – Mark Jun 26 '21 at 15:40

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For example, when $i = 4$ and $t = 2$, then $N\setminus\{i\} = \{1,2,3\}$.

$$\begin{align*} \sum_{j\in\{1,2,3\}}(x_{4,j,2} + x_{j,4,2}) &= 1\\ \text{or}\\ (x_{4,1,2} + x_{1,4,2})&\\ +(x_{4,2,2} + x_{2,4,2})&\\ +(x_{4,3,2} + x_{3,4,2}) &= 1\\ \end{align*}$$

peterwhy
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