Problem
Prove the following properties associated with multistage Omega networks using different-sized building blocks:
(a) Prove that the number of legitimate states (connections) in a k )k switch module equals kk.
(b) Determine the percentage of permutations that can be realized in one pass through a 64-input Omega network built with 2 >: 2 switch modules.
(c) Repeat part (b) for a 64-input Omega network built with 8 x 8 switch modules.
(d) Repeat part (b) for a 512-input Omega network built with 8 x 8 switch modules.