What is this notation, similar to the binomial coefficient?

Question

I've come across this notation:

$$\left\{\begin{eqnarray}n\\m\end{eqnarray}\right\}$$

The only other info I have about this notation is that $\left\{\begin{eqnarray}4\\2\end{eqnarray}\right\}=7$

What's the name of this notation and what is it used for?

Thanks

Answer 1

Maybe you're using Stirling numbers of the second kind, where $\displaystyle{n\brace k}$ denotes the number of ways to partition a set of $n$ objects into $k$ non-empty subsets.

You can use {n\brace k} to produce ${n\brace k}$ and \displaystyle{n\brace k} to produce $\displaystyle{n\brace k}$.

An example of a 'real world' application of these numbers can be found in this MSE question which asks how many rooks can be placed on a triangular chessboard so that none of them are attacking each other.

Answer 2

Stirling numbers of second kind, the number of partitions of a set of $n$ objects into $k$ non-empty subsets.