Definition 1.10 (Combinatorial line). A combinatorial line in $X^{n}$ is a set of the following form:

{(x_{1}, \dots, x_{n}) \in X^{n} : \exists I \subseteq [n], a_{i} \in X, I \neq \emptyset, x_{i} = a_{i} \forall i \notin I, x_{i} = x_{j} \forall i, j \in I} .