Riffle shuffle permutation

Summary

In the mathematics of permutations and the study of shuffling playing cards, a riffle shuffle permutation is a permutation of a set of $n$ ordered items that can be obtained by a single riffle shuffle, in which a sorted deck of $n$ cards (increasing top-to-bottom) is cut into two packets and then the two packets are interleaved (e.g. by moving cards one at a time from the bottom of one or the other of the packets to the top of the sorted deck). As a special case of this, a $(p,q)$-shuffle, for numbers $p$ and $q$ with $p+q=n$, is a riffle in which the first packet has $p$ cards and the second packet has $q$ cards.