Math 4370 Combinatorics
Homework
Spring 2016
Reading assignment
The week of April 1921: 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 2628: We will finish subsection 5.1.3, and then discuss section 5.2.
The week of May 36: We will discuss subsection 5.4.1. Don't forget that we meet on Friday 11:3012:50 (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 selfconjugate 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 doublyrooted tree corresponding to the function found below,
and (b) finding the function [n]>[n] corresponding to the doublyrooted 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