Transpositions, Simple Transpositions, Inversions and Sorting
A 2-cycle is known as a transposition. A simple transposition in Sn is a 2-cycle of the form (i i + 1).
For a permutation p in Sn, a pair (i, j)∈In is a permutation inversion, if when i<j, we have p(i) > p(j).
Every permutation can be written as a product of simple transpositions; furthermore, the number of simple transpositions one can write a permutation p in Sn can be the number of inversions of p and if the number of inversions in p is odd or even the number of transpositions in p will also be odd or even corresponding to the oddness of p.
Read more about this topic: Permutation Group
Famous quotes containing the word simple:
“The old-fashioned idea that the simple piling up of experiences, one on top of another, can make you an artist, is, of course, so much rubbish. If acting were just a matter of experience, then any busy harlot could make Garbo’s Camille pale.”
—Helen Hayes (1900–1993)