# Math 4370 Combinatorics Homework

## Dr. Duval

The week of April 19-21: On Tuesday, we discussed subsections 5.1.1 and 5.1.2. On Thursday, we finished up subsection 5.1.2, and started subsection 5.1.3.

The week of April 26-28: We will finish subsection 5.1.3, and then discuss section 5.2.

The week of May 3-6: We will discuss subsection 5.4.1. Don't forget that we meet on Friday 11:30-12:50 (in Bell Hall, room 125), instead of Thursday, this week.

### Homework

1.10: 1, 2b, 4, 5, 6.
1.10: 12, 14, 15, 21, 24.
1.10: 13, 30, 32, 33, 39, 41.
2.10: 1, 2, 3, 4, 5.
2.10: 7 [S(n,2) only], 8, 9.
2.10: 2 [with correct use of "distinct"], 10, 14, 15.
2.10: 18 (just the self-conjugate partitions of 19), 19, 21, 30.
2.10: 11, 12, 34, 36, 38.
2.10: 40, 41, 42, 43.
3.10: (you must use generating functions to solve these problems to get credit) 3, 4, 5, 6, 7.
3.10: 9, 11, 21, 23.
5.10: 4, 5, 6, 9, 13, due Thursday, April 28.
5.10: 10, 15, due Friday, May 6.
Cayley: Illustrate your understanding of the proof of Cayley's theorem by (a) finding the doubly-rooted tree corresponding to the function found below, and (b) finding the function [n]->[n] corresponding to the doubly-rooted spanning tree found below, due Friday, May 6.

Cayley stuff here:
```
(a)

i | f(i)
---+-----
1 |  6
2 | 10
3 |  1
4 | 10
5 |  6
6 | 10
7 |  2
8 |  6
9 |  2
10 |  3

(b)
4
|
|
8
|
|
5 -- 10 -- 1 -- 6 -- 9
|         |
|         |
7         3
|
|
2
```
start vertex is 4; end vertex is 9