(p,q) shuffle


Let p and q be positive natural numbers. Further, let S(k) be the set of permutationsMathworldPlanetmath of the numbers {1,,k}. A permutation τS(p+q) is a (p,q) shuffle if

τ(1)< <τ(p),
τ(p+1)< <τ(p+q).

The set of all (p,q) shuffles is denoted by S(p,q).

It is clear that S(p,q)S(p+q). Since a (p,q) shuffle is completely determined by how the p first elements are mapped, the cardinality of S(p,q) is (p+qp). The wedge product of a p-form and a q-form can be defined as a sum over (p,q) shuffles.

Title (p,q) shuffle
Canonical name pqShuffle
Date of creation 2013-03-22 13:33:59
Last modified on 2013-03-22 13:33:59
Owner mathcam (2727)
Last modified by mathcam (2727)
Numerical id 7
Author mathcam (2727)
Entry type Definition
Classification msc 20B99
Classification msc 05A05
Synonym shuffle
Related topic ShuffleOfLanguages