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.