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I've come across this notation:


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?


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I find it slightly disappointing that with the vast knowledge we have here, all three answers do little more than link to wikipedia. – user1729 Jun 18 '14 at 10:33
There is a Stirling numbers, which I added to your post. If you are interested in them then you might want to browse through the questions there. – user1729 Jun 18 '14 at 10:44
up vote 12 down vote accepted

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.

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Any chance of an application? It would make your answer complete...(for example, they can be used to find certain generating sets of certain semigroups). – user1729 Jun 18 '14 at 10:25
Can you elaborate your answer by providing a real life example of its usage? Thanks... – Tunk-Fey Jun 18 '14 at 10:29

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

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