Is there a commonly accepted notation for k-subsets? The question says it all. I have once seen the following notation used for $k$-subsets of a set $S$ but I failed to verify that it is commonly used and I was also unable to find any evidence for a different commonly used notation.
$$ [ S ]^{k} := \{ X \mid X \subseteq S \wedge | X | = k  \} $$
Is this notation commonly used? Is there a more commonly used notation? Does this notation clash with another commonly used notation? If there is no commonly used notation would this be a sensible choice because it is similar to the Cartesian product $S^{k}$ but I have not seen $[S]$ used in the context of set theory (besides $[n]$ as the set of ordinals up to $n$)?
 A: The notation $[S]^k$ is standard in set theory, and appears frequently in discussions of the partition calculus, among other places. Some authors use $S^{[k]}$ instead, to avoid conflict or double brackets when the set $S$ is also an interval. 
The notation is also used in the context of finite combinatorics, but not so commonly. The most standard expression in that context seems to be $\binom Sk$.
By the way, in finite combinatorics and other contexts, the notation $[n]$ tends to be used to represent the set $\{1,2,\dots,n\}$. Note that, on the other hand, in the context of set theory, $n=\{0,1,\dots,n-1\}$.
A: Yes, the notation is perfectly common and acceptable. It is used often in set theory (especially in contexts where one talks about colorings of $k$-subsets).
As my usual tip here goes, if you're unsure of the validity of certain notations, just add the definition before using it.

If $S$ is a set, we shall denote by $[S]^k$ the set of $k$-subsets of $S$, that is, $[S]^k=\{A\subseteq S\mid |A|=k\}$.

Or something like that.
