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
Famous quotes containing the words group, theory and/or aspects:
“It’s important to remember that feminism is no longer a group of organizations or leaders. It’s the expectations that parents have for their daughters, and their sons, too. It’s the way we talk about and treat one another. It’s who makes the money and who makes the compromises and who makes the dinner. It’s a state of mind. It’s the way we live now.”
—Anna Quindlen (20th century)
“The whole theory of modern education is radically unsound. Fortunately in England, at any rate, education produces no effect whatsoever. If it did, it would prove a serious danger to the upper classes, and probably lead to acts of violence in Grosvenor Square.”
—Oscar Wilde (1854–1900)
“It is always a sign of an unproductive time when it concerns itself with petty and technical aspects [in philology], and likewise it is a sign of an unproductive person to pursue such trifles.”
—Johann Wolfgang Von Goethe (1749–1832)