I'm am developing some notation for a model and am needing to denote the concatenation of two strings. However, I'm not sure if there is a standard way to do this.
Let's take a simple example. Say I have variables $X$ and $Y$ which take the values of $a$ or $b$ (in the context I'm working with, $a$ and $b$ are strings with a specific value) and $Z$ which is a concatenation of $X$ and $Y$. Now, I want to define concatenation, $X + Y = Z$, such that,
$a + a = aa$
$a + b = b + a = ab$
$b + b = bb$
I have two questions here.
1) I don't want to use the "+" symbol to denote concatenation and was wondering if anyone knows if there is a standard mathematical notation for this.
2) I am also unsure whether one calls this unordered concatenation (as $a+b = b+a$) or ordered concatenation (as $a$ is to always come before $b$ in the concatenated string $Z$).