#### CSCI 7000 - Cryptography - Spring 2010

### Problem Set #1

#### Due: Feb 3rd, 2010 at 4pm

1. How many permutations are there on the set A={1,...,10}?
2. Go look up "cycle notation" for permutations (if you don't already know
it). Write down all permutations, in cycle notation, on the set B={1,2,3}.

3. What is the probability that a random permutation on set A (see problem 1)
is represented by one cycle?

4. (Harder.) What is the probability that a random permutation on A is
an involution?

5. Learn Python. (Just learn a little bit... we'll use it later.) You can
do this online or buy a book if you like. As a warm up, write a program to
generate a random permuation on A and output it in cycle notation. Please
run your program 5 times and include the output and along with your source
code.

6. Run you program again, but on the set C={1,...,1000}. Do not output
your random permutation this time; instead quietly run your program
10,000 times and give the average length of the longest cycle.