Homework Assignment Twelve Quick Answers

1. 9.1.4 

2. 9.1.12 pi2 and pi7 don’t commute

3. 9.2.4 (1/4)[2**64+2*2**16+2**32]

4. 9.2.10 (1/2)[3*2**(n-1)+3*2**(n/2-1)]

5. 9.3.4 a. 1/7[3**7+3+3+3+3+3+3]

6. 9.3.14 permutations transform subsets into 
subsets. A two-coloring of the points in the 
set identifies a subset and its complement, and 
a coloring (a subset) is invariant if the 
coloring is constant across cycles. Hence the 
result.

7. 9.4.2a,b
a) 
1/6[(b+w)**6+2(b**6+w**6)+2(b**3+w**3)**2+(b**2+w**2)**3]; 4 
(b is similar..)

8. 9.4.10a b**2w**2r+b**2wr**2+bw**2r**2

9. 9.4.12

10. (extra credit - done in class)

-- RobbieMoll - 12 Dec 2006