(p,q) shuffle
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Let p and q be positive natural numbers. Further, let S(k) be the set of permutations of the numbers 
. A permutation τ in S(p + q) is a (p,q)shuffle if
,
.
The set of all (p,q) shuffles is denoted by S(p,q).
It is clear that
Since a (p,q) shuffle is completely determined by how the p first elements are mapped, the cardinality of S(p,q) is
The wedge product of a p-form and a q-form can be defined as a sum over (p,q) shuffles.
This article incorporates material from (p,q) shuffle on PlanetMath, which is licensed under the GFDL.
