Let <math>p</math> and <math>q</math> be positive natural numbers. Further, let <math>S(k)</math> be the set of permutations of the numbers <math>\{1,\ldots, k\}</math>. A permutation <math>\tau</math> in <math>S(p+q)</math> is a (p,q)shuffle if <math> \tau(1) < \cdots < \tau(p) \,</math>, <math> \tau(p+1) < \cdots < \tau(p+q) \,</math>.

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  • Let <math>p</math> and <math>q</math> be positive natural numbers. Further, let <math>S(k)</math> be the set of permutations of the numbers <math>\{1,\ldots, k\}</math>. A permutation <math>\tau</math> in <math>S(p+q)</math> is a (p,q)shuffle if <math> \tau(1) < \cdots < \tau(p) \,</math>, <math> \tau(p+1) < \cdots < \tau(p+q) \,</math>. The set of all <math>(p,q) </math> shuffles is denoted by <math>S(p,q). </math> It is clear that <math>S(p,q)\subset S(p+q). </math> Since a <math>(p,q) </math> shuffle is completely determined by how the <math>p</math> first elements are mapped, the cardinality of <math>S(p,q)</math> is <math>{p+q \choose p}. </math> The wedge product of a <math>p</math>-form and a <math>q</math>-form can be defined as a sum over <math>(p,q) </math> shuffles.
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  • 4176 (xsd:integer)
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  • p,q) shuffle
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  • Let <math>p</math> and <math>q</math> be positive natural numbers. Further, let <math>S(k)</math> be the set of permutations of the numbers <math>\{1,\ldots, k\}</math>. A permutation <math>\tau</math> in <math>S(p+q)</math> is a (p,q)shuffle if <math> \tau(1) < \cdots < \tau(p) \,</math>, <math> \tau(p+1) < \cdots < \tau(p+q) \,</math>.
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  • (p,q) shuffle
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