I am looking for a compact way to represent a group of vectors for which each vector contains no two elements that are the same.
$$\textbf{y} \in R^n \quad | \quad y_i \neq y_j \quad \forall \quad y_i, y_j \in \textbf{y}$$
I believe this part $y_i, y_j \in \textbf{y}$, is not correct, I am looking for some way to represent the meaning of an element of a vector
what about $\{y\in\Bbb{R}^n| \forall 1 \le i < j \le n, y_i\ne y_j\}$?