Group Theory Aspects
In mathematics, a perfect shuffle can be considered to be an element of the symmetric group.
More generally, in, the perfect shuffle is the permutation that splits the set into 2 piles and interleaves them:
Formally, it sends
Analogously, the -perfect shuffle permutation is the element of that splits the set into k piles and interleaves them.
The -perfect shuffle, denote it, is the composition of the -perfect shuffle with an -cycle, so the sign of is:
The sign is thus 4-periodic:
The first few perfect shuffles are: and are trivial, and is the transposition .
Read more about this topic: Faro Shuffle
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