]> 0.4 Stirling Numbers of the Second Kind

## 0.4 Stirling Numbers of the Second Kind

OK but I knew all these things already.

Here is a slight but useful modification. In D5 instead of the instruction above put '=d\$1*d4+c4', and copy that into a huge rectangle. The dollar sign, \$, will cause the index that follows it to remain constant. Thus when you copy this into other rows and columns, d\$1 will be the element of that column in the first row.

When you again put 1 in c4 you get numbers called "The Stirling numbers of the second kind" .

Binomial coefficients count the number of subsets of an $n$ element set having $k$ elements in them. The Stirling number for arguments $n$ and $k$ here counts the number of partitions of a set of $n$ elements into $k$ disjoint blocks.

Exercises:

0.6 Set this up on your own machine. Solution

0.7 Binomial coefficients count the number of subsets of an $n$ element set having $k$ elements in them. The Stirling number here counts the number of partitions of a set of $n$ elements into $k$ disjoint blocks. Prove these two statements. Solution

0.8 Invent a good question for this spot.