String/vector concatenation symbol
Personally, I would use \oplus
for this. I would think of it as a direct sum of two vectors (as a member of the direct sum of two vector spaces).
You can use two pluses joined together, which is rather intuitive
\documentclass[a4paper]{article}
\newcommand{\concat}{\ensuremath{+\!\!\!\!+\,}}
\begin{document}
$a \concat b$
\end{document}
Another symbol is ||
\[ p\|q=p b^{l(q)}+q \]
The \|
command gives a double vertical bar.
Since a vector in R^2 is written (1, 2), it would make sense to concatenate two vectors a and b as (a,b).