Group Theory 

Group Theory is the mathematical study of permutations.


There is also a card trick
equivalent to this permutation called a "perfect shuffle." The order
of the deck will repeat after log
_{2} N shuffles.


The mathematical permutation and card trick can also be represented spatially as a set of mappings.



The "grand tour" or "perfect shuffle" has a special property that can be best be seen spatially. These permutations are also topologically complete. In other words, all the inputs can reach all the outputs. 

