Publish On: 2019-03-22

# Ben joy

Total Post: 542

## Question: Describe the permutation function

Reply On: 2013-10-07

# Mjay Jollay

Total Post: 0

## ANS: Describe the permutation function

A one-one function whose domain and the range is the same set, the set being finite, is called a permutation function. For example, let S = {1, 2, 3} be a finite set, then there are 3 ! = 6 permutation functions p

Let p be a permutation function and i < j be a pair of elements in its domain such that p (i) > p (j), then p is said to have an inversion. For example if S = {1, 2} and the permutation function is p

_{1}, p_{2}, p_{3}, p_{4}, p_{5}, p_{6}defined from S to S. Let us explain the permutation functions by means of the above table.**Inversion**Let p be a permutation function and i < j be a pair of elements in its domain such that p (i) > p (j), then p is said to have an inversion. For example if S = {1, 2} and the permutation function is p

_{2}, then we notice from the above table that 2 < i p(2) > p(1) and as such p_{2}has one inversion. Obviously, p1 has zero inversion. In other words, an inversion is said to take place if in a permutation 3, 1 and 2, we have the couples (1, 2) which gives one inversion.Like Us On Facebook for All Latest Updates