Homework #6, Due April 8 at the beginning of class.
Solution sets must be correct, legible, and complete for full marks.

Chapter 7: 13, 25, 45, 49, 59.

Let A be a fixed subset of {1,2,...,n} of size k and let T(n,k) denote the number of labelled forests on n nodes with k trees with the property that the nodes of A are in different trees. Derive and solve a recurrence relation for T(n,k). This was the problem that I gave in class.

In class I gave a handout with a formula for the number of unlabelled digraphs. Explain why that formula is correct.