Named variables in math

Question

In my publication I have a case where it is a bit difficult to keep track of indices / variables, because of I have multiple of them and some are replaced with actual integers. Let me give an example:

Fully written, I have

$x_{i,t}$

but since I would need to put an $i$ into the index of nearly every symbol, it is much more elegant to refrain to do so and just write

$x_{t}$

However, now I have the case that $t$ is indeed 1, not just any integer, and that in this particular formula I need to bring back the $i$. How can I make this clear? I would like to write use named variables (similar as I am used from programming), so along the lines

$x_{i,t=1} = \ldots$

Is this valid notation? Is there a better, concise alternative?

Also, how about if this issue does not arise for index notation, but in the parenthesis:

$y(j=2,s=4)$

instead of

$y(2,4)$

Is this valid notation?

Answer 1

The solution is not to be lazy and to keep the $i$ subscript even though it is repeated. As you can see from your own examples, any other approach is horrible.

Answer 2

I suggest to mantain the $x_{i,t}$ notation. If you have to explicitly write some value for $t=1$, just write $$ x_{i,1} = \dots $$ Similarly, for $i=3$ then $$ x_{3,t} = \dots $$

Sometimes (such as in case of iteration numbers) it is also useful to use apexes and parenthesis: $$ x^{(k)}_{i,t} = \dots $$

In these cases, I always use parenthesis in order to distinguish it from squared, cubic, $\dots$ values: $$ x^2_{i,t} = x_{i,t}\,x_{i,t} $$