---
tag: NDTRC3H9BY
kind: concept
name: Riffle shuffle permutation
aliases: [p-q-shuffle, shuffle-permutation]
sources:
  - wikipedia: en:39949298@r1373717204
    locator: Riffle shuffle permutation
    note: adopted
    mention: wikipedia://en/39949298
    sections: [Summary]
same_as:
  wikidata: Q13846433
  wikipedia: Riffle shuffle permutation
inventory: [8ST18KFD1H]
---

## Summary

In the mathematics of [[permutations|05RWFKVTJ7]] 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.