Chapter 2, Problem 53E

To determine

To find: A one to one correspondence that is constructed between the permutations of the sets $\left\{1,2,\mathrm{...},n\right\}$ and the towers $A_0\subset A_1\subset A_2\subset \cdot \cdot \cdot \subset A_n$ where $\left|A_k\right|=k$ for $k=0,1,2,\mathrm{...},n$.