# (p,q) shuffle

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Let and be positive natural numbers. Further, let be the set of permutations of the numbers . A permutation in is a **(p,q)shuffle** if

The set of all shuffles is denoted by

It is clear that

Since a shuffle is completely determined by how the first elements are mapped, the cardinality of is

The wedge product of a -form and a -form can be defined as a sum over shuffles.

*This article incorporates material from (p,q) shuffle on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.*