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 very definition of the real becomes: that of which it is possible to give an equivalent reproduction.... The real is not only what can be reproduced, but that which is always already reproduced. The hyperreal.”
—Jean Baudrillard (b. 1929)
“... 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)
“... we all know the wag’s definition of a philanthropist: a man whose charity increases directly as the square of the distance.”
—George Eliot [Mary Ann (or Marian)