]>
|
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 element set having elements in them. The Stirling number for arguments and here counts the number of partitions of a set of elements into disjoint blocks.
Exercises:
0.6 Set this up on your own machine. Solution
0.7 Binomial coefficients count the number of subsets of an element set having elements in them. The Stirling number here counts the number of partitions of a set of elements into disjoint blocks. Prove these two statements. Solution
0.8 Invent a good question for this spot.
|