Usually a tuple is written like $(x, y, z)$, e.g. like $$\DeclareMathOperator{\argmax}{argmax} a*, b*, c* = \argmax_{a,b,c}( \dotso\text{long line}\dotso ). $$
For my publication I don't have space for a long tuple like that in the line. So I would like to write:
$$ \begin{pmatrix} a* \\ b* \\ c* \end{pmatrix} = \argmax_{a,b,c}( \dotso\text{long line}\dotso ). $$
Is it valid notation to write a tuple upright like that?
Would it also be valid to change $$ f(x | a,b,c) $$ into $$ f\left(x\ \left|\ \begin{pmatrix} a \\ b \\ c \end{pmatrix} \right.\right)? $$
Traditionally, by a very useful convention, the vector $(a,b,c)$ is identified with the column matrix (or column vector) \begin{bmatrix}a\\b\\c\\ \end{bmatrix}
Unfortunately, many people nowadays think that matrices should be delineated with parentheses, not brackets. Consequently, they think that $(a,b,c)$ is a row vector (or row matrix), so they write $(a,b,c)^T$ to mean the above ordinary column vector, to avoid extravagant use of vertical space.
Since you have the opposite problem, with plenty of vertical space but restricted horizontal space, I commend to you the traditional convention, using nice straight matrix brackets, as in the display above, to denote your vector $(a,b,c)$ .