We will try to answer the above question by analyzing the stopping times (which is the time after which the deck of cards is completely random) of the card shuffling process.
The torus is one of the most important geometrical objects in mathematics. As a topological space it is just a product of two circles. The is a natural continuous mapping from the real plane to the torus which is called the exponential map.
Suppose there is a graph G, whose vertices are letters in an alphabet A and in which adjacency means that the letters can be confused in a transmission.
