CSC 482/582 SUMMER 2012 Assignment #5

Due June 27 by midnight.

1. Explain how (5.30) is a "special case" of (5.55). 

2. What binomial coefficient identity arises from the equation
   (1+z)^{-m} (1+z)^m = 1?

3. What is the generating function of n^3?

4. Let A(x) be a polynomial of degree m whose coefficients are 
   a[0],a[1],...,a[m].  Prove the following identity:

   SUM( A(k)*binomial(n,k)*D(n-k), k=0..n ) =
   n! SUM( a[i]*B(i), i=0..m )

   Here D(j) is the number of derangements of j items,
   B(i) is the i-th Bell number.

5. Choose your project topic and tell me what it is via email
   (do this right away!).   Some of you have done this already;
   no need to do it again.