Tagged Questions
1
vote
1answer
32 views
Determining Stirling number
In the first part of the question I was asked to find the exponential generating function for $s_{n,r}$, the number of ways to distribute $r$ distinct objects into $n$ (a fixed constant) distinct ...
5
votes
2answers
177 views
Why does $S(n,k)=\sum 1^{a_1-1}2^{a_2-1}\cdots k^{a_k-1}$?
I've been trying to get back into some combinatorics, and in my reading, I find that
$$
S(n,k)=\sum 1^{a_1-1}2^{a_2-1}\cdots k^{a_k-1}
$$
where the sum is taken over all compositions ...
