Cycle Notation - Definition

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)

    Scientific method is the way to truth, but it affords, even in
    principle, no unique definition of truth. Any so-called pragmatic
    definition of truth is doomed to failure equally.
    Willard Van Orman Quine (b. 1908)

    ... if, as women, we accept a philosophy of history that asserts that women are by definition assimilated into the male universal, that we can understand our past through a male lens—if we are unaware that women even have a history—we live our lives similarly unanchored, drifting in response to a veering wind of myth and bias.
    Adrienne Rich (b. 1929)