Specifically, I refer to the following set:
$$ \left\{ x\in\mathbb{Z}\mid a\leq x\leq b\right\} $$ where $a\in\mathbb{Z}$ and $b\in\mathbb{Z}$ such that $a<b$.
Alternatively, this can be written as $\mathbb{Z}\cap\left[a,b\right]$, but it still looks a bit ugly.
I am looking for a more compact notation, such as perhaps $\mathbb{Z}_{a}^{b}$. The problem with this is that it is ambiguous, as it can be interpreted as a $b$-dimensional vector space over $\mathbb{Z}_{a}$.
Is there perhaps a good way to compactly write this in a formula?
The notation $[[a,b]]$ for ${\mathbb Z}\cap [a,b]$ is quite well spread, at least in French litterature. For the special case of $\{1,\dots,n\}$, combinatorists often use $[[n]]$.