Definition
Let be a finite set, and
be distinct elements of . The expression
denotes the cycle σ whose action is
For each index i,
where is taken to mean .
There are different expressions for the same cycle; the following all represent the same cycle:
A 1-element cycle such as (3) is the identity permutation. The identity permutation can also be written as an empty cycle, "".
Read more about this topic: Cycle Notation
Famous quotes containing the word definition:
“The man who knows governments most completely is he who troubles himself least about a definition which shall give their essence. Enjoying an intimate acquaintance with all their particularities in turn, he would naturally regard an abstract conception in which these were unified as a thing more misleading than enlightening.”
—William James (1842–1910)
“Perhaps the best definition of progress would be the continuing efforts of men and women to narrow the gap between the convenience of the powers that be and the unwritten charter.”
—Nadine Gordimer (b. 1923)
“Although there is no universal agreement as to a definition of life, its biological manifestations are generally considered to be organization, metabolism, growth, irritability, adaptation, and reproduction.”
—The Columbia Encyclopedia, Fifth Edition, the first sentence of the article on “life” (based on wording in the First Edition, 1935)